The k-domination number of a graph G=G(V,E), γk(G), is the least cardinality of a set XV such that any vertex in VX is adjacent to at least k vertices of X.Extending a result of Cockayne, Gamble and Shepherd [4], we prove that if δ(G)n+1nk1, n1, k1 then, γk(G)npn+1, where p is the order of G.