In this paper we prove the following result. Let A be a semisimple H*−algebra and let T : A → A be an additive mapping satisfying the relation (n + 1)T(xnm+1) = T(x)xnm + xmT(x)x(n−1)m + · · · + xnmT(x), for all x ∈ A and some fixed integers m ≥ 1, n ≥ 1. In this case T is a two-sided centralizer.