Let ƒi, i = 1, … k, be complex-valued multiplicative functions satisfying the conditions
where αi ε C,
(i = 1, …, k), with some 0 < ϱ ≦ 1. Under these conditions we prove that
moreover, if each fi satisfies (*) with C = 0, then there is ϱ1 > 0, such that
holds, where 3 < v < logAx. As a corollary we prove some results about the mean-value of multiplicative functions.