It's Wednesday afternoon and Molly Jong-Fast is meant to be in Dublin to promote her new novel Normal Girl - only, unfortunately, Molly suffers from a terrible fear of flying. She made it as far as London from New York, but the thought of having to get on a another plane, even just to Dublin, is too much for her.

The phobia would be bad enough on its own but for Molly it's that much worse, because Molly's mother, Erica Jong is terribly famous for one particular book, a book called Fear of Flying.

"I know, everyone thinks it's terribly funny. Except me, I don't think it's funny at all. I think it's the worst thing in the world," Molly says mournfully down the phone.

It's not as if Jong-Fast doesn't have enough interest focused on the family connection already - when the daughter of the woman who coined the phrase "the zip-less fuck" in the 1960s produced a novel herself at the age of 22, the media started salivating. In fairness, Normal Girl does rather seem to invite prurient attention. It's the story of 19-year-old Miranda, who grew up in New York with famous parents; she consumes a phenomenal amount of drink and drugs but no food, then crashes into rehab.

Miranda describes her mother as "someone who knows how to stick out her neck so her jowls, the jowls of an ageing socialite, are stretched out, obscured by her damaged brown hair". Miranda says of herself: "Children of famous people are like communism - better in concept than in practice."

Perhaps it's unfair to blur the lines between fact and fiction, but there are undoubted parallels between Molly's life and that of Miranda. She has said she started smoking pot at 12 or 13 and then did pretty much everything else before settling on an addiction to cocaine. Then there's the struggle with bulimia, which Molly has written about, describing how the actress Joan Collins said Molly couldn't go on Valentino's yacht because she was too fat, and how Molly responded by bingeing and vomiting - until four years ago. There are, of course, the famous parents (Molly's father, Jonathan Fast was a screenwriter).

"I think I started Miranda because she was someone I hated but who I also wanted to be. I mean, she really pushes the envelope, she's like my alter ego in that she's like me only more so. She says the things I wish I could think to say at the time." That is as far down the autobiography line as Jong-Fast will go - she determinedly describes her own childhood as "like any other childhood" and her relationship with her mother as "we're really good friends". Her character, Miranda, realises she has reached the end of the line after a near-death experience, while Molly is slightly more vague about the reason for her own clean-up: "I got some notion that there might be a God. I realised I wasn't immortal. It was a number of different things."

Growing up, she didn't really realise how her family was different or just how famous her mother was. "We were kind of sheltered from it. I was kind of a distracted child. I read a lot. I had my head in the clouds." She never read Fear of Flying and didn't even know what it was about until a school-friend pointed out that her mother wrote dirty books. She says she has read about 200 pages, but jokes that it's "disgusting" before pointing out that she's joking. Her mother has read Normal Girl and "really likes it . . . although she did say it was very dark".

Erica is right; Normal Girl is fairly disturbing - but it's also very good. Firmly setting its sights on the genre presided over by Jay McInerney and Brett Easton Ellis, it's fast-moving, well-written and slick - perhaps the most endearing point is when Miranda points out that: "There's no point in describing an AA meeting: it's like a car accident or the Grand Canyon, always lost in the translation." The most endearing thing about Molly Jong-Fast is her glee in the whole process of writing.

"When I first wrote this book I thought `Oh, I'm going to go on tour and everyone will think I'm fabulous' but now that I'm actually doing it I realise I definitely prefer the life of work . . . I just love it when I sit down at my desk, which is this really cool old antique door, and it's just me at my computer, writing and smoking cigarettes and drinking coffee. It makes me feel so much better than anything else. It's the time I get to be myself and say exactly what I want to say. I even love the sick bits like the stress. I love it all."

Her typical writing day starts at 7 a.m. and she will do constant rewrites, reducing some 800 pages down to 300. She attributes her work ethic to her grandfather, the communist screenwriter Howard Fast - "Now he was obsessive" - but is also very clear-sighted about her own privileges. "I had so many advantages that I didn't want to squander them. I really wanted to write the very best novel I could. Because of who my mother is I had the opportunity to get my book published and I wanted to use it well. I think children of famous parents can think their parent's fame is their own. You have to be very clear about who is who."

There are times when the roles between mother and daughter seem almost reversed. Molly bemoans about her own "un-artistic" punctuality; "I'm always five minutes early for everything but then I've grown up with someone who's always 25 minutes late. I know how annoying that is." Talking about the difference between her mother's generation, as chronicled in Fear of Flying and her own, as chronicled in Normal Girl, she is anxious about sexual freedom, about how much more lethal drugs are "these days", and about the complacency of youth.

She believes the feminist movement is "fragmented" and dominated by people more interested in their careers than equal rights. She blames that on herself and her peers, pointing out that "a generation that never lived without freedom, doesn't know what it has to lose. Our generation is in a precarious place because there is no impetus for us to move forward and if we're not moving forward, we're moving backward".

Still, for the moment Molly Jong-Fast is happy - her book is out, the critical reception has been good and all in all, it's "a Cinderella story - no, really, it is. Because I had dyslexia when I was little, and I thought I was just a stupid moron who wouldn't amount to much. Now I'm thinking all my terrible thoughts about myself might not be true. It's a real happy ending. Except for the turbulence on the flight home, that's definitely not a happy ending at all."

Normal Girl by Molly Jong-Fast is published by Sceptre, price £10 in the UK.