As usual, he is dressed outlandishly - in black Armani maternity T-shirt with tails, and matching airline slippers - but his performance is immaculate. Anyone who feared he'd come back spouting crass West-Coast therapisms is soon reassured: the vigour of Connolly's profanity and the sharpness of his eye are undiminished. After a ritual disembowelment of Britain's current leaders, and a quick resume of recent ecclesiastical and parliamentary sex scandals, he swiftly buckles down to the personal and above all the physical observations which are his strongest suit.
No nook or cranny of the human body is too personal for Connolly to find comic inspiration in it. A rare sighting of his own scrotum during (hey, Hollywood]) a yoga exercise sets off a delightful meditation on what a horrific spectacle that part of the male physiognomy must present to women encountering one for the first time - 'Rodney, for God's sake] The most awful thing has crawled out of your arse]' His remorseless scatology is not only very funny, it also reassures his audience. He's now living with the stars, but his mind is still in the gutter.
After all these years, Connolly's tendencies to crease up with hilarity at his own most basic jokes - 'Old Macdonald was dyslexic, ee oh ee oh I' - ought to be irritating, but, somehow, it isn't. He can make you laugh out loud at something that probably isn't very funny, just by virtue of the physical pleasure he gets from the idea that it might be.
For all his bluffness, it is Connolly's willingness to appear vulnerable that makes people warm to him. His family reminiscences start out plain funny - a gluttonous aunt is thrown across a drawing-room by an exploding toaster into which she was attempting to cram a jam-laden crumpet - but end up very touching. Other comedians might discuss their dead father, but not in the poignant, self-questioning way Connolly does. He remembers his dad punching him, or moaning about forgetting his driving glasses, and himself mentioning new developments in prescription windscreens for cars, but then being unable to tell him this was a joke for fear of being thought a smartarse. Now he pictures the elder Connolly trying to sell such a car, or just driving in it, with passers-by thinking he had an enormous head. No one could wish for a sweeter epitaph.
A lot of people think Rory Bremner has a big head too, but on stage - amid the Essex gulls of the elegant Southend Cliffs - he seems rather humble. Bremner lost his Scottish accent to fit in at posh English schools, but soon learnt to pick up others. Last year the BBC's determination to keep him in a light-entertainment straitjacket pushed him to Channel 4, where he has since made a startlingly successful transformation from boyish purveyor of sports commentators and weathermen to diamond-hard political satirist. People who have not seen this for themselves still find it hard to believe.
A live show is a big challenge for a TV impressionist. Without changes of make-up, wigs and coloured contact lenses it is sometimes hard not just for the audience but also for Bremner to keep up with who he is meant to be. His composure and skill are immense, but there are a few awkward moments. His confident 'does anybody here listen to Radio 4?' is met with a fairly deafening silence. What price his dazzling Cliff Morgan in such a cold, hard world.
The construction of show- cases for impressionistic virtuosity can be a tiring business, for performer and audience alike, but Bremner's comedians' theme-park is a masterpiece of the genre. Gentleness and savagery live happily side- by-side in his show. Bremner's is a sedate crowd - husbands and wives look at their partners before smiling - but Bremner hits them with some pretty tough stuff when in angry mode, and they don't seem to mind. 'Green-belt development, motorways, racism,' he proclaims in an impeccable Ashdown parade-ground bark, 'they're all part of life for today's Liberal Democrats.'
Billy Connolly: Hammersmith Apollo, W6, 081-741 4868, Mon to Sat, then 23-28 May. Rory Bremner: St Albans Arena, 0727 844488, tonight, then touring.