This article deals with the relationship between ordinary and p-modular characters of the group SU(3, p), parallel to the treatment of SL(3, p) in J. E. Humphreys, Ordinary and modular characters of SL(3, p), J. Algebra72(1981), 8–16. Here we denote by SU(3, q) the special unitary subgroup of SL(3, q2), where qis a power of the prime p; the notation SU(3, q2) is perhaps more standard, but we want to emphasize the comparison with SL(3, q). Our main conclusion is that the decomposition behavior is essentially the “same” for both groups, in a sense to be made more precise below.