We prove that the frequencies of the oldest, second-oldest, third-oldest, … alleles in the stationary infinitely-many-neutral-alleles diffusion model are distributed as X
1, (1 − X
2, (1 − X
1)(1 − X
3, …, where X
3, … are independent beta (1, θ) random variables, θ being twice the mutation intensity; that is, the frequencies of age-ordered alleles have the so-called Griffiths–Engen–McCloskey, or GEM, distribution. In fact, two proofs are given, the first involving reversibility and the size-biased Poisson–Dirichlet distribution, and the second relying on a result of Donnelly and Tavaré relating their age-ordered sampling formula to the GEM distribution.