Alvin Ailey American Dance Theatre, Prog 1, Sadler's Wells

Alvin Ailey dancers have been dancing about survival, grit, positivity and joy in the Lord for half a century now, and even though the parents of last night’s dancers may not have been born when Ailey did the unthinkable and launched a black dance company in the dark days of 1958 America, the company still evidently has an urge to rejoice running in its veins.

The regular returns of AAADC to Britain - and there’s a big nationwide tour this time - are constant wake-up calls to the spirit. How can you sit down-in-the-mouth about anything at all when you’re watching a girl haughtily unfolding her shoulders and power rippling down her arm into a curling hand, or swishing her big skirt and prancing high on bare feet as if walking on mountain-tops?

There is such vim and innocence in the movement style that’s evolved at Ailey’s - a ballet-meets-showtime-meets-salsa-meets-pure-bolshie that sweeps through the body without a single inhibition. Ailey girls must be some of the most beautiful creatures on a stage anywhere, and that may be the feminist influence of the long-serving artistic director Judith Jamison, an Amazonian figure on the same inspirational level as Martha Graham was to her dancers.

But the company has been treading water creatively for some time now under Jamison - Ailey himself has remained the core of the repertoire, and impossible to beat, hence the permanent presence in every performance of his ever-buoyant 1960 riverside gospel celebration Revelations. As we saw last night, this piece is as unquenchable as the sunrise, witty, sweet-natured and surprisingly powerful in its attack on the soul.

So the succession to Jamison, who’s 67, has been of supreme importance to American dance, AAADC having now as iconic a presence in US cultural life as Mount Rushmore. And last night we heard the new voice, the man who last spring was announced as her designated successor, a non-Ailey dancer, Robert Battle - and though he is presumably trembling in his boots at taking on this monumentally political job, I think he looks promising.

The two short pieces we saw were, for once, about men rather than women: an agonised 2008 solo, In/Side, set to a great Nina Simone song, and a combative male sextet, The Hunt, created in 2001 for the Parsons Company, where Battle was a dancer. In/Side is a remarkable example of extreme dancing, with the self-sacrificing Samuel Lee Roberts (see main image above) thrashing like a shackled prisoner to "Wild is the Wind", Simone’s haunting song brooding on bereavement (“Give me more than one caress” is one heartrending line). The Hunt is a formally arranged ritual combat of three against three, dressed in Japanese-style divided skirts, which though it runs out of invention as the men tire, is carried on the swell of violently pounding steel drums of the French percussion phenomenon, Les Tambours du Bronx (see a striking video here), and is marvellously lit by Burke Wilmore for maximum drama.

Both pieces offer an overdue update for the Ailey men, something more about today’s urban New York man than archetypes. It’ll remain to be seen whether Battle can develop his sense of self into the popular large-scale ensembles that an accomplished school-of-Ailey choreographic studio has been successfully producing for decades.

Pieces like last night’s opener, George W Faison’s 40-year-old Suite Otis, whose skin-tight pink satin outfits and waggling bottoms look cutely retro on today’s athletically muscled men - in 1971 it was a dude look, I guess. What hasn’t dated in the least is the magical draw of Otis Redding’s cracked-pepper voice, and those seething, melancholy, erotic songs of his. This has loads of intriguing period references, a Martha Grahamish bride in black, folksy skirt-swinging to the Stones' "Satisfaction", and African-American witticisms I couldn’t imagine from any other dance company: the lindy-hop jiving, some hilarious cheek-to-cheek tittuping, and a sociable larkiness that seems to come from generations of church upbringing.

Ronald K Brown is another Ailey dancer-turned-choreographer - his 2009 Dancing Spirit (pictured right by Paul Kolnik) looks more high-minded in intention, self-consciously passing gestures down the line like wisdom and lore, with flounced Caribbean dresses and a lot of arabesques and pirouettes. There’s again a striking musical track (this one involving Duke Ellington, Wynton Marsalis and Radiohead among others), but a lot of activity on stage looks formless, leaving you to seek out dancers with charisma, and while great veteran dames like Renee Robinson and Linda Celeste Sims continue to magnetise, I wish I could name the girl in the baggy purple pantaloon shorts and the tall guy in the sarong trousers.

There are two programmes offered on a nationwide tour which will give a larger audience than ever the chance to be uplifted.

• Alvin Ailey American Dance Theatre is at Sadler's Wells till 25 September; then tours to Nottingham Royal Centre, 1-2 October; Birmingham Hippodrome 5-6 October; Plymouth Theatre Royal 8-9 October; Cardiff Wales Millennium Centre 12-13 October; Bradford Alhambra 15-16 October; Edinburgh Festival Theatre 19-20 October and Newcastle Theatre Royal 22-23 October

Watch an extract from a 1982 performance of Revelations at New York City Centre: