Saul Bellow's Heart … If you've ever read anything about the great man's private life you might suppose the title of his son's memoir is intended ironically, or that it's one of those deliberately incongruous couplings, like The Pope's Rhinoceros, meant to arouse a slightly incredulous fascination. Even if you know only the books themselves, you might be surprised by the singling out of that particular organ. Bellow's novels watch and listen like few others. They scratch, sniff, taste and think about the world with an astounding sensory intelligence. They follow their characters through the mazes of their lusts and desires with uncanny clairvoyance. But they aren't, quite, moving. Not in the intimate way of Dickens, and not really in the grand way of Tolstoy, either. Heart, in other words, isn't the first thing you think of when you think of Saul Bellow.

The exception is Seize the Day, the painfully touching story of a son's thwarted craving for his father's love. It was written soon after the death of Bellow's own father, Abe, a failed bootlegger turned coal merchant, who beat his children and derided Saul's literary aspirations. Greg Bellow (Saul's eldest son) sees the novel as autobiographical, and tells two family stories that illuminate both the parental harshness and the filial vulnerability. One is a sour little story Saul himself liked to tell, of being weaned at three or four after his father, irritated by Saul's neediness, "opened his own shirt and exposed his useless nipple". The other is Greg's own childhood memory of witnessing a terrible argument between Saul and Abe. "Driving away from his father's house, Saul started to cry so bitterly he had to pull off the road. After a few minutes, he excused his lapse of self-control by saying, 'It's okay for grownups to cry.' I knew his heart was breaking. I knew because of the bond between my father's tender heart and mine."

His implicit contention is that the place to look for Saul's heart is somewhere in the nexus of these father-son dramas as they played out across his writing and life. The raw feeling of Seize the Day would seem to support him, though the fact that Bellow reversed the personality types of father and son, making Dr Adler a sleek success and his son a shambling failure, complicates the life/art parallel. You can read Adler and Tommy as hard old Abe and tender young Saul. But you can also read the book, more prophetically, as an unsparing portrait of Bellow himself as the successful, self-protective artist-parent warding off the emotional demands of his difficult dependants. Not that Greg Bellow, a genial-sounding psychotherapist with a solid career behind him, is a straightforward match for the aggrieved and inept Tommy, but being Saul Bellow's son clearly hasn't been easy for him. The "bond" he speaks of was severely strained when his father disappeared into the second of his five marriages, and thereafter it seems to have been honoured, at least on Saul's side, as much in the breach as in the observance.

Good memoirs often arise out of complex motives, and the way these reveal themselves can be a significant part of the drama. By his own account, Greg's reason for embarking on this project was simply to preserve his memories of his father. To some extent the book does indeed function as a curatorial exercise. The broader narrative framing the memories is fairly well known – Saul Bellow's boyhood spell in a TB ward, the serial intellectual mentors (or "reality instructors" as he liked to call them), the Paris epiphany that released the exuberant voice of Augie March, the early Trotskyism morphing through the turmoil of the 60s into the conservatism of the later years – but there are details and anecdotes here that only a family member could have supplied, and they enrich our sense of the private man behind the public career. I like knowing, for instance, that on his own son's being weaned, the first thing the delighted Saul fed him was a pickled herring; that during Saul's Reichian phase, father and son used to roar like lions at approaching subway trains; that winter and summer alike, Saul would emerge from writing sessions in his study drenched in sweat; that his sister fell asleep in the front row during his Nobel speech in Stockholm (I connect this snippet to the fact that relatively few women seem passionate about Bellow's work); that his connoisseurship of accents was such that he could place Greg's new girlfriend precisely in the West Rogers Park neighbourhood of Chicago; that throughout their lives, Saul and his siblings would speak Yiddish when discussing family business … Small as they are, these details have a tang of reality that Bellow himself would surely have appreciated.

But beyond this dutiful cataloguing of memories, Greg's book is also the record of a long, complicated and painful oedipal struggle of his own. Dividing his father into the "young Saul" who gave him his own liberal values, and the "old Saul" who became increasingly self-centred and reactionary, Greg stakes out a territory for himself from which he can admire one and stand up to the other, while loving – and feeling loved by – both. He comes across as a decent guy, who has genuinely made peace with his father's personal failings (which included a capacity for stinging remarks: "Saul commented that I had turned the misery of my childhood into a career …"). But clearly there are things that still rankle. The end of the book, in particular, goes in for some mild score-settling over the steely manoeuvres by which Janis Freedman Bellow (Saul's fifth wife) wrested control over Saul's life and legacy, and her apparent attempt – briefly successful – to turn the old man against his sons.

These pages leave a slightly sour taste, but it would be a mistake to regard them as the sole, or even the most important, impetus for the memoir. There is an unresolved animus at the book's core, but to my mind it's an interesting one, if underexplored.

Early on, Greg writes of his dismay, during his father's funeral, at all the young writers jostling to get in on the act: "After all, he was my father." He offers his sense of having had a sacrosanct private relationship violated by these "self-appointed sons and daughters", as the point of departure for his own literary journey. The implication is that he has moved on. But he still sounds sore about it at the end: "I have resigned myself to sharing my father with his literary public because I have no real choice."

Fair enough. It must be hard to feel the ties of blood being superseded by those of literature. But it points to a flaw in his otherwise lucid appraisal of his father. This is his failure, or unwillingness, to examine the extreme nature of the demands art makes on a serious artist, or to consider that these demands might necessarily come first, with everything else, including the evolution of the artist's own personality, compelled to follow.

But that's perhaps another book. As for this one, a measure of its success is that it makes you think about such things in the first place.

• James Lasdun's Give Me Everything You Have: On Being Stalked is out from Cape.