IT COMES AS a bit of surprise, although it shouldn't. The American writer Jeffrey Eugenides arrives for an event at Dublin City Gallery the Hugh Lane on a Saturday afternoon within weeks of the publication of his engaging third novel, The Marriage Plot, to find the elegant space busy with anticipation.

Many people in the audience are already holding copies of the large red book. More will be purchased after the reading. But also well represented are battered paperback copies of The Virgin Suicides, from 1993 and Middlesex, from 2002. "This is the first time I've had a back list," says Eugenides, who is good-natured and wry, softly-spoken and not given to panic. "Those books were slow builders."

He is a relaxed individual with a funny little 19th-century-style moustache who manages to notice everything without appearing wary. He is currently teaching creative writing at Princeton University, New Jersey, "but it's only one day a week. I'm a full-time writer. Pretty soon after The Virgin SuicidesI was able to live from my writing. Before that, when I was writing it, I was working in an office."

Nothing is typical about him. "I don't have a message," he says. "My novels aren't like that." He is not a commentator. But he does have a plan. The Virgin Suicides, in which five young sisters each decide to kill themselves, is about as dramatic a study of teenage ennui as one could encounter. "Looking back on it now, perhaps a cover with broken dolls was not the best image; it might have put readers off." He seems slightly distracted and admits to being tired but certainly looks, seems and sounds far younger than his age – he turned 51 in March. "When I look at my students, these incredibly bright, young, twentysomething students, I suddenly feel very old," he says, but doesn't appear too bothered by it. "It's really my hair; it's just not there any more."

Now back in the US having spent five years on a fellowship in Berlin, during which he wrote much of Middlesex, the novel that won him a Pulitzer Prize, Eugenides, despite his Greek heritage, is an American – if one now slightly detached from his country. "I came back – we came back, my wife and I – because of our mixed-race daughter. My wife is Japanese-American. This is something that is so much more part of America. We felt it was better for her to grow up in the States. I liked being in Germany; I like Europe a lot. But we came back. I see myself as American. But, aside from being away, America has changed."

Perceptions of him as a writer have also changed. "This time there has been more of an emphasis on me." Some of the US reviewers were more inclined to add biographical detail to their responses to the novel. "I think that that is something that happens; after a few books [the reviewers] think it's time to be harder on you because they know you." In common with Mitchell, one of the three major characters in The Marriage Plot,Eugenides had been to India, but he is not an autobiographical novelist. "That's true, I'm not. I think you might draw on your own experience or more your memory of something when you are describing a place or a person, or something that happens to a character that may also, in some form, have happened to you, but I don't write autobiographically."

There was also an element of speculation surrounding this new novel, due more to the legacy of The Virgin Suicidesthan to Middlesex.Aside from the dramatic impact made by a debut novel such as The Virgin Suicides, profound not only for its content but for the stylistic maturity and the use of a collective narrative – a chorus of bemused middle-aged men recalling their teenage selves lusting after the enigmatic Lisbon sisters – Eugenides is somehow very different. He is an original whose vision is not particularly radical.

THEN THERE WAS the nine-year wait for Middlesex, a saga, sprawling and complex, the tracing of a rogue gene suspended between sexes. It was classic, and comic, and tragic, a human dilemma spanning 70 years. His prose possessed lyric force. And then another silence, a further nine years, as if Eugenides was writing under some kind of spell. Instead he was living a very normal life because he is about as normal as a writer can be. There is no angst, no intensity, no big claims. He is not out to tell the story of the United States, nor to either expose or solve its many problems. Instead he evokes the US in a way similar to that of John Updike. Eugenides writes stories.

"A fictional idea comes to you, like there is this girl studying English literature, and then you start to write the story." He makes it sound so simple. The Marriage Plotmay well be seen as simple, almost conventional, and the language is less literary, more detailed than that in his other novels. A privileged Wasp girl studying English at college sets her sights on a difficult guy, well aware that she also has a devoted suitor hovering eagerly in her wake. The three students are educated and sexually aware yet are still inhabiting the shelter of the extended childhood provided by college. "And childhood," says Eugenides, "is something that lasts a long time in the States: look at our presidents."

In his two first novels, the story was all. But this time it was different for him. The characters drive the plot; their actions, doubts and hopes become the story. “This book was the first time I tried to go deep into my characters – deep as in psychologically deep. I did get into their heads and needed to know how they thought, what they were thinking about. I think that that is the hardest thing for a novelist to attempt. I mean, you want it to sound true, real – true in a way that memoir isn’t. You know that in a memoir people write something and people ask ‘Is that true?’ That can’t happen in a novel, because in a novel everything is true, everything is real because it is – that’s the story you’re writing.”

This explains why he set out to make the dialogue between the characters sound so intensely personal as to be real. The extract he chose to read at the Hugh Lane gallery illustrated this intention. In it, Leonard, the elusive, depressed biology major who the heroine, Madeleine, decides is the guy for her, goads her with personal questions intended to prod her into a reaction that he hopes will challenge her middle-class sensibilities.

If nothing else, The Marriage Plot, set largely in the US in the early 1980s, is about American-style social class. Madeleine is from a comfortable background: her father is a college president; her mother keeps a social diary. Our heroine is likeable, as well as being good-looking, popular, naive and relatively privileged. Eugenides feels Leonard is interested in Madeleine because she is wealthy. "That's the thing about her that attracts him," he says. The depiction of social class in the novel is not only one of its themes; it is one of its strengths. Eugenides says he learned all about infiltrating social class himself. After Brown University, in Rhode Island, he attended Stanford. There he was, a non-Wasp guy from Detroit who could break into that social world, "if only on the fringes", because he was educated and astute to the cultural references.

Of course Eugenides likes Madeleine: who couldn't? The first big risk she takes is to enrol on a course in French literary theory taken by a professor who "didn't run the class so much as observe it from behind the one-way mirror of his opaque personality". Also taking the course is Leonard Bankhead, a character with a name worthy of Pynchon. The narrative is well at ease with literary and cultural references, which never threaten to overpower it. In ways the book is a celebration of the 19th-century novel, with its theme of marriage as the ultimate goal. Eugenides is an admirer of the tradition. "I wanted to write about marriage, but in our time it no longer has the permanence it used to have when people mainly did stay married. Now divorce is so common, or people don't get married at all." But this is not to say that Eugenides has set out to provide a defence of the institution. He doesn't work like that. Nor is The Marriage Plota satire, although it is often very funny.

His approach to humour is different from that of many US writers, who push the comedy of situations to the limit. His new novel has relatively little in common with Jonathan Franzen's Freedom, also published in the UK by Fourth Estate. "He is writing about the present, and even offers an update at the end of the book, whereas I tend to set my books in the past."

The 1980s setting of Brown is close to his own experience. While he is sympathetic to his main characters and concedes that his initial idea for the book was largely colonised by Madeleine, while Mitchell, the man of God, so determined to be saintly, fails in the most human way, Eugenides appears quite ambivalent about Leonard. On one level Leonard, the man of science, appears to be a truth-teller, poised to dismantle pretence. Eugenides crushes this notion with an uncharacteristically blunt smirk: “He’s full of shit.” Whether he is or not, Leonard develops into a riveting study of a manic depressive.

There is no denying that The Virgin Suicideswas the definitive hard act to follow. But Eugenides did, with a very different book in Middlesex. Now he has done something quite arresting. The Marriage Plotis very unusual, in that Eugenides has achieved the near-impossible in drawing 21st-century readers into feeling protective towards the three protagonists. It could be that readers identify with, recognise and remember elements of themselves in these characters – some feat for a novelist who is not openly manipulative.

SOME CRITICS SUGGEST, mistakenly, that Eugenides is deconstructing the 19th-century novel. Instead, he appears to admire those seminal novels of personal struggle by writers as diverse as Austen, Eliot and Tolstoy. “I was a modernist, a postmodernist. I had read Joyce – all before I ever came to the 19th-century novels, which I love. I think there is something remarkable about how we struggle with feelings, emotions. I think of Levin and I think, Yes.”

Eugenides has written three very different novels. The Virgin Suicideswill remain iconic. He looks quite serious for a moment, and then says "It is interesting how that book appears to reinvent itself with each generation. Mothers of daughters come up and tell me how much their daughters understood it, what it meant to them." And The Marriage Plot,with its laughs and tears, and its exploration of the underworld of depression, has an unusual quality – a kindness not often evident in contemporary fiction. Again Eugenides appears almost grave, and reiterates: "What you make up in a novel really is true within its fictional world. A novel has to be true and real. I really believe that."

The Marriage Plot

is published by Fourth Estate, £14.99