The cover of the proof copy of T Singer (originally published in Norwegian in 1999) is given over entirely to a photograph of the 76-year-old author, brooding on the unremarkable fact of having his picture taken, with a tangle of ash-white hair that is all but indistinguishable from the smoke of the cigarette he’s sucking on. Almost a piece of anti-PR, it’s the perfect expression of how Dag Solstad presents his work to the world. Who else would title a book Novel 11, Book 18, as though to alert readers that far from attempting to achieve that elusive publishing grail, a breakout book, there is nothing special about this one, that it’s just more of the same?

Solstad’s same, however, is unlike anyone else’s, even the younger Norwegian writers such as Karl Ove Knausgård and Per Petterson whose international success has helped create a climate in which we might be newly receptive to his wonderfully uncompromising conception of the novel.

Solstad's protagonists drift through the novels named after them, brooding on their lot by fixating on very little

T Singer begins with Singer remembering a trivial incident from his childhood when his uncle caught him acting in “an uncouth manner” in a shop. The loop of anxiety induced by this memory feeds into another loop in which we learn of the multiple variants of the first sentence of a book Singer never got around to writing. At 34, he decides to become a librarian in the small town of Notodden. On the train there he meets Adam, the head of Norsk Hydro, who invites him back to his splendid villa where a rather “peculiar evening” unfolds. Sloshing back vast quantities of booze, Singer listens as the boss delivers an epic lecture on the history of his company, the region and the relationship between philosophy and industry. Nothing comes from this – the two drinkers never meet again – except for notes on a system of betting which, Adam assures Singer, is guaranteed to make money. Singer begins his work as a librarian, and marries a woman with a young daughter whom he ends up raising on his own, back in Oslo. The climax of the book – spoiler alert! – involves a potentially “awkward situation” involving cinema tickets.

There are holes in this summary, just as “in every novel there is a big black hole which is universal in its blackness”. When we arrive at this hole, in this novel, Solstad says that his “language ceases when Singer’s pondering ceases. Yet that does not make us identical.”

Quite so. But Singer is very similar to Solstad’s other narrators and protagonists who drift through the novels named after them, brooding on their lot by fixating on very little. In Shyness and Dignity a teacher, having been unsettled in class by a textual detail in Ibsen’s The Wild Duck, erupts into a life-changing fit of rage provoked by his… umbrella. In Professor Andersen’s Night the eponymous professor believes he has witnessed a murder in the apartment opposite. Needless to say, the edge-of-the-seat suspense generated by this Hitchcockian set-up leaves the reader slumped on his sofa.

Wherever they start, Solstad’s characters find a way to establish themselves in a low-key, middle-aged life in which melancholy and contentment are almost indistinguishable. They live as Philip Larkin might have done if he’d got a job in Telemark instead of Hull. There is a feeling of destiny at work, reinforced by the absence of any kind of causality whereby this happens because that happened. “What had he done with his life? This was the thought of a man who, not for a single moment, harboured any conviction that his life could have been any different.”

If the drift has its own relentlessness – a feeling of the accidentally implacable – then that is rooted in the circuitry of Solstad’s prose. (In turn the author depends on certain types of character to generate the prose in which they appear: “literary protagonists who are capable of setting the tone in my novels”.) The Solstadian long sentence feeds back into itself, meandering with the aimless inevitability of a river heading towards the sea. Thomas Bernhard would seem to be an influence, but instead of the pent mania that animates the narrators of Extinction or Concrete Solstad lulls the reader with a wanly insistent gentleness. Bernhard has us in stitches. Solstad’s humour is the opposite of hysterical. This is what laughter might feel like in a language lacking the word for it – not because nothing is funny but because everything is. And while one would never apply the adjective “lovely” to anything by Bernhard, that is the word that comes to mind as Singer introduces his daughter to the cosmopolitan delights of Oslo. Boarding a tram, Singer recognises a celebrity:

“‘Did you see who that was?’

Isabella shook her head and looked down.

‘That was the weather man,’ said Singer solemnly.”

Later Singer observes his daughter and her friends in “a young-lady circle of loveliness and laughing” from which he will become ever more excluded. Larkin comes to mind again, looking down at “the churches ornate and mad/ In the evening sun. It is intensely sad.”

At one point Singer notices how a certain couple “shared the same perception of reality”. Solstad’s construction of reality is uniquely his own. That may be why the writer Lydia Davis taught herself Norwegian solely by reading his work. For my part, I confess that this verbal world of his – mad, sad and funny – often teeters on the brink of being boring. But that feeling merges into another that is quite thrilling as the behavioural possibilities of the novel are subtly and fundamentally enlarged.

In his Paris Review interview Solstad said that, having “perfected” a certain form of novel with T Singer, his work was over. This liberated him to… continue working! First published in Norwegian in 2006, Armand V is one of the works from what he calls this “overtime” phase of his career. Fittingly, Solstad describes it as a series of “ongoing but distorted footnotes to an unwritten novel”. That sounds experimental but it soon feels as comfortable as a pair of old suede shoes. After about 30 pages Solstad mentions how, in the composition of a novel, he becomes conscious of the point, sometimes 30 or 40 pages back, when “the whole thing went off the rails”. He then starts over from that point, implicitly to get it back on the rails. It’s an extraordinary claim. I mean, the idea that, for Solstad, a novel needs rails. In his weirdly hypnotic way isn’t this what he is always railing against?

Geoff Dyer’s latest book is The Street Philosophy of Garry Winogrand.

• T Singer and Armand V by Dag Solstad are published by Harvill Secker (£14.99) and Vintage (£11.99) respectively. To order a copy for £12.74 or £10.19 go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99