In the context of generalized Orlicz spaces, the products X-Phi 1 circle dot X-Phi 2 and X-Phi 1 circle times X-Phi 2 are studied and conditions are obtained under which these spaces are contained in a suitable space X-Phi. These imbedding results (inequalities) are in a sense sharp and for the case X = L-1, the conditions are even necessary and sufficient. Moreover, a new Holder type inequality is proved.