SAN ANTONIO — Gregg Popovich has never worried that Tim Duncan will lobby management to get rid of him behind his back. They are as tethered to each other as this city is to the Alamo. For 15 of his 16 years as the Spurs’ coach, Popovich has told assistants, “We have the easiest job in the N.B.A. because of Tim Duncan, because of who he is and the way he conducts himself.”

But here in the land that N.B.A. time forgot — where there is no “I” in team, only in Tim — folks still face a universal chronological challenge. If growing apart is not a problem, growing old is. Duncan, the most minimalist superstar of the modern professional basketball era, will turn 36 on April 25. Popovich, the only N.B.A. coach Duncan has had and with whom he has won four championships, is 63.

Though reports of the Spurs’ competitive death were greatly exaggerated after they lost in the first round of the playoffs to Memphis last spring after a 61-victory regular season, the question persists even as their quest for a fifth title continues: how much life do they really have left in them?

“As for us being dead, it’s that way every year,” Duncan said with a shrug. “For a while now, it’s been, ‘We’re getting too old.’ I guess it’s going to happen eventually. Somebody’s going to be right.”