NEW YORK (AP) ― “Time Waits for No One,’’ the Rolling Stones sang in 1974, but lately it’s seemed like that grizzled quartet does indeed have some sort of exemption from the ravages of time.

At an average age of 68-plus years, the British rockers are clearly in fighting form, sounding tight, focused and truly ready for the spotlight at a rapturously received pair of London concerts last month.

On Saturday, Mick Jagger, Keith Richards, Ronnie Wood and Charlie Watts hit New York for the first of three U.S. shows on their “50 and Counting’’ mini-tour, marking a mind-boggling half-century since the band first began playing its unique brand of blues-tinged rock.

And the three shows ― Saturday’s at the new Barclays Center in Brooklyn, then two in Newark, New Jersey, on Dec. 13 and 15 ― aren’t the only big dates on the agenda. Next week the Stones join a veritable who’s who of British rock royalty and U.S. superstars at the blockbuster 12-12-12 Superstorm Sandy benefit concert at Madison Square Garden. Also scheduled to perform: Paul McCartney, the Who, Eric Clapton, Bruce Springsteen & The E Street Band, Alicia Keys, Kanye West, Eddie Vedder, Billy Joel, Roger Waters and Chris Martin.

The Stones’ three U.S. shows promise to have their own special guests, too. Mary J. Blige will be at the Brooklyn gig, as well as guitarist Gary Clark Jr., the band has announced. (Blige performed a searing “Gimme Shelter’’ with frontman Jagger in London.) Rumors are swirling of huge names at the Dec. 15 show, which also will be on pay-per-view.

In a flurry of anniversary activity, the band also released a hits compilation last month with two new songs, “Doom and Gloom’’ and “One More Shot,’’ and HBO premiered a new documentary on their formative years, “Crossfire Hurricane.’’

The Stones formed in London in 1962 to play Chicago blues, led at the time by the late Brian Jones and pianist Ian Stewart, along with Jagger and Richards, who’d met on a train platform a year earlier. Bassist Bill Wyman and drummer Charlie Watts were quick additions.

Wyman, who left the band in 1992, was a guest at the London shows last month, as was Mick Taylor, the celebrated former Stones guitarist who left in 1974 ― to be replaced by Wood, the newest Stone and the youngster at 65.

The inevitable questions have been swirling about the next step for the Stones: another huge global tour, on the scale of their last one, “A Bigger Bang,’’ which earned more than $550 million between 2005 and 2007? Something a bit smaller? Or is this mini-tour, in the words of their new song, really “One Last Shot’’?

The Stones won’t say. But in an interview last month, they made clear they felt the 50th anniversary was something to be marked.