In this paper, the iterates of (α, q)-Bernstein operators are considered. Given fixed n ∈ N and q > 0, it is shown that for f ∈ C[0, 1] the k-th iterate T k n,q,α (f ; x) converges uniformly on [0, 1] to the linear function L f (x) passing through the points (0, f (0)) and (1, f (1)). Moreover, it is proved that, when q ∈ (0, 1), the iterates T jn n,q,α (f ; x), in which {j n } → ∞ as n → ∞, also converge to L f (x). Further, when q ∈ (1, ∞) and { j n } is a sequence of positive integers such that j n /[n] q → t as n → ∞, where 0 ≤ t ≤ ∞, the convergence of the iterates T jn n,q,α (p; x) for p being a polynomial is studied.