We never even learn their last name. But we come to know the family at the center of Adam Haslett’s powerful new novel, “Imagine Me Gone,” as intimately as if it were our own. When the book opens, brothers Alec and Michael are holed up at a cottage in Maine during a winter thaw — and something, we gather, has gone terribly wrong.

Before we can figure out what, Haslett circles back to introduce us to the parents, Margaret and John. Their story begins in 1963 when Margaret, an American working at a library in the London suburbs, meets John, an exuberantly talkative Englishman, at a “gin-drinks” party thrown by mutual friends, “everyone in ties and dresses.” The couple becomes engaged to be married, but when Margaret returns from a visit home for Christmas, she learns from a flatmate that John has been admitted to the hospital.

“Has he had an accident?” she asks.

It isn’t that kind of hospital. When Margaret goes to visit him, she reports that John is “so drained of spirit I barely recognized him.” A tactful English doctor calls John’s condition “an imbalance”: “You could say his mind closes down. It goes into a sort of hibernation. He needs rest and sometimes a bit of waking up.”

Margaret marries him anyway. They have three children — Michael and Alec, as well as Celia, and move to the United States. John’s manic depression is kept at bay for 15 years, but of course it returns, as Margaret, and the reader, suspects it must.

“Imagine Me Gone” is the story of this family across the decades — a family that is bonded and riven and bonded again by mental illness. The story is narrated in alternating chapters by each of the five members, and when it is Michael’s turn to speak — he recounts an insane family cruise that becomes so preposterous — and so hilarious — that we realize what John has recognized, too: “[He] talks as fast as can be, not questions but endless invention, his imagination running out ahead of him, to make sure everything stays in motion, that he doesn’t get stuck.” John’s affliction runs in the family.

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Michael is the center of the novel and certainly Haslett’s most original character: An inconsolable baby, a precocious and verbal teenager, a disco and house-music fanatic who is rigidly politically correct and falls hopelessly in love with black women (one of them a lesbian). In one chapter he offers a wiseass history of his medications and their effects: Luvox, Paxil, Serzone, Anafranil, Celexa, Effexor, Lexapro, Wellbutrin . . . you get the idea. For the reader, as for his family, Michael is strangely dear, utterly maddening and ultimately heartbreaking.

Mental illness is familiar territory for Haslett, whose debut story collection from 2002, “You Are Not a Stranger Here,” was a finalist for both the Pulitzer Prize and the National Book Award. He revisited some of the same themes in his 2010 novel, “Union Atlantic,” in which a retired Yankee schoolteacher living alone hears the voices of Cotton Mather and Malcolm X channeled through her dogs. In “Imagine Me Gone,” Haslett strips away the real-estate squabbles and financial-world intrigues of that novel to look at one family in the round, observing how John’s and Michael’s issues ripple out — rendering Celia compulsively responsible, an adult before her time, and making Alec a control freak who prefers anonymous sex with men to actual relationships.

“Imagine Me Gone” is slow to get started — we’re dropped into a plot in progress and must pick up the family’s story at a few different moments in its history. Stick with it. Once Haslett has you, you’re along for the ride with Margaret, John, Michael, Celia and Alec: as absorbed by — and powerless over — their fate as they are.