This note deals with a q-dimensional stochastic vector process x(t) = {x1 (t), …, xq (t)}, satisfying certain stated general conditions. For such a process, there is a representation (1) in terms of stochastic innovations acting throughout the past of the process. The number N of terms in this representation is called the multiplicity of the x(t) process, and is uniquely determined by the process. For a one-dimensional process (q = 1) it is known that under certain conditions we have N = 1. For an arbitrary value of q, this note gives conditions under which we have N ≦ q.