In nearly all mainstream continuities, it is understood that Superman's aging is slowed down by an extreme factor. I don't have references, but there have been a few occasions where Superman avoided a romance with Lois precisely because he would remain young while she grew old & died. References to this were made in non-mainstream comics as well, such as Kingdom Come (spoiler-ish description of the scene below):
When Diana first contacts a retired Superman, he is living in self-exile up at the Fortress of Solitude. A bitter Kal-El has severed all ties with humanity, apparently following the death of his wife (Lois). When Diana expresses her sympathy, Kal responds with the detached sentiment humans die, they grow old. The context insinuates "They grow old, WE do not." However, it should also be noted that Kal-El has minor gray streaks in his hair at the temples, generally a sign of aging.
Also, in Superman: Red Son, there are references to Superman's aging:
Near the end of the book, after Superman's "death", hundreds of years have passed and Kal-El's narrative notes that he's starting to feel the passage of time. His powers are duller and he's not as strong or fast as he used to be. Of course, this may also have to do with the fact that the Earth's sun is slowly turning red due to its own age.
The reduction in aging is directly tied to his abilities under a yellow sun, so it is presumed that Kryptonians under their native sun would age & die naturally. Also, Kal-El's aging is likely unique since he is the only Kryptonian who has absorbed the rays of a yellow sun since childhood. He aged normally (by human standards) until around 30, so obviously the aging factor didn't kick in until then. A mature Kryptonian who later moved to a yellow sun - say, at age 30 - would likely have to absorb the radiation for decades before their aging would slow, but they could potentially be a 60-year-old for a few centuries (IF the radiation affects adult physiology the way it affected Kal-El during youth).