Arts: Every which way but forwards: Whither painting? All over the place, it appears. Tim Hilton

SINCE THE days when it was run by the old Arts Council, the Hayward has had a poor record of supporting contemporary art, so the exhibition 'Unbound: Possibilities in Painting' is welcome. The selector is the painter and critic Adrian Searle, assisted by Greg Hilty (previously at the Riverside and now a Hayward curator). I cannot discover Hilty's contribution - perhaps it was administrative or banausic. For months the art world has been talking about 'Adrian's show' and wondering how he would manage. Rather well, I think. Here's a display of new painting that's like the man himself: genuinely art-loving, curious about anything that comes its way, debonair and elusive.

I've always wanted to know what his beliefs are, but Searle continues to mystify. He fills the galleries with artists he likes, and writes both an introduction to the show and comments on the individual painters. I am intrigued by all this but really none the wiser - and as I write a suspicion comes to mind that this is Searle's intention; not so much to instruct as to play on our sense of curiosity, to make us wonder why people paint as they do and not to demonstrate that they paint well.

There are 14 artists in the exhibition and I do not see what they have in common, except that many of them are given to deft but uncompleted statements. There are people in the show with a heavier touch, but they are not in keeping with the general mood. One is Paula Rego, a surprising choice since she is now such a part of the British establishment. Another is Fiona Rae who, like Rego, puts more into her pictures than is needed, with shapes and squiggles dashing here and there as though under constant but undirected attack. She needs to simplify her work and do something about her inert colour, so dependent on puce, grey and maroon.

Elsewhere, though, lightness of manner is the norm. Luc Tuymans (born 1958) is an Antwerp artist whose slight, almost anonymous paintings turn out to be full of menace. His pictures are small, not at all like each other and appear to refer to emotions that are like traps, separating their victims from the rest of the world. Tuymans' Candycontainer is unsettling in just this way. Its artist doesn't symbolise and brood, like so many Belgian painters. He just casually lets you know that something is behind you, and that probably it's malevolent.

Has Searle been searching Belgium on his holidays? Another small-scale painter he has discovered is Raoul De Keyser, now in his sixties, who has lived and painted all his life in the provincial town of Deinze. He's more abstract than Tuymans and even more diffident. Perhaps he feels the weight of the modern abstract tradition in the Low Countries. His pared- down compositions recall such art. At the same time he indulges in some eccentric handling, as if to say that classicism has no sway over him.

Such work has its value but one can't say that it shows the 'possibilities' of the exhibition's title. Neither Tuymans nor De Keyser suggest that painting's future should have a grand engagement with the spirit of our times. Neither does the Dusseldorf artist Imi Knoebel, whose bare plywood pictures and heartless parodies of de Stijl are conceptual paintings of a particularly useless sort.

Rather better is the Germanic expressionism of Michael Krebber. His messages are obscure, but at least he suggests that painting can deal with tragedy, that it's not a matter of self-regarding nuance or entertainment.

Paradoxically, the one piece in the show that approaches the grand manner is not in any strict sense a painting. Jessica Stockholder uses rubber sheeting, lights, flex, straps, pillows and a pile of refrigerators to make her Fat Form and Hairy: Sardine Can Peeling. This enormous, entertaining piece barges its way through the gallery wall and the ramp that leads to the first-floor rooms. But it is emphatically not an installation. Stockholder (born 1959) has made a number of such pieces in America, and to judge from photos they are all inspired by painting and with the feeling of two-dimensional art. She's a latter-day Rauschenberg, but crazier.

Searle's selection can be interpreted as either generous or erratic. Of course he couldn't have covered all of contemporary art, and actually begins quite close to home. Zebedee Jones, who presents talented minimal paintings with thick, lush surfaces, has been picked up from the Chelsea MA course. Peter Doig is another graduate from Chelsea, where Searle teaches. The prizewinner at the last John Moores exhibition, he's a deservedly popular artist at the moment. He gives us more of his nostalgic but bright, photo-based memories of Canada. Can he paint without photographs to help him? He ought to try.

Unbound is a pleasant but not epoch-making exhibition. It doesn't fulfil the Hayward's obligations toward new British art, having none of the excitement of the old Hayward Annuals. Nor can it tell us what's happening in world art. It suggests however that London ought to have an international biennale or triennale.

So many other countries host big global shows, but we don't. Yet we have the British Council, with an expert art department. The Hayward's director, Henry Meyric Hughes, formerly ran that department. In his position I'd think of a triennale, getting the first one up in 1997 and with a really major exhibition to mark the year 2000.

Hayward Gallery, SE1, 071-261 0127, to 30 May

(Photograph omitted)