The Rolling Stones European Tour comes with staggering statistics. We are informed that it takes 53 trucks and a staff of 260 to transport the enterprise around the continent and, inscrutably, that the tour weighs 350 tons. But one figure is more mind-boggling than them all. The collective age of the four remaining Rolling Stones is 237. They are, as Jagger unironically sings during a version of Muddy Waters's I'm A Man, "way past 21".

For the band's live show to work, the audience is required to suspend their disbelief and swallow the line that The Rolling Stones themselves have been peddling since the early 1970s - that they are the world's greatest rock'n'roll band. Sometimes, that's hard to do. As the show opens, they seem shambolic and rusty. They thrash sloppily through Heartbreaker and It's Only Rock and Roll, the sound muddy and indistinct.

When the Rolling Stones play badly, you are left with a pantomime of leathery skin, terrible clothes and ridiculous behaviour. These days, Keith Richards has the sort of face you normally see halfway up a church wall with water gushing from its mouth. He sports a variety of hideous shirts, which flap open as he bends over his guitar to solo, and what looks like a vast white bandage over his thinning hairline. He seems a model of dignified maturity next to Mick Jagger, who gropes a backing vocalist during Honky Tonk Women, and rushes around the stage with his arms extended, flapping his hands, like a man in the gents who has just discovered the hand-drier isn't working.

However, as you are preparing to write the Rolling Stones off as a superannuated embarrassment, something gels. Tumbling Dice staggers forth, still charmingly louche. Richards' appearance gives his solo spot, Before They Make Me Run, an added degree of defiant poignancy. Better still, they repair to a tiny stage in the centre of the arena, and begin playing for their lives: Brown Sugar's arrogant swagger, a ferocious Neighbours. At moments like that, you can almost believe the hype.