We study the direct incoherent energy transfer in systems, in which the molecules involved in the transfer process are attached to ideal (Gaussian) polymers, randomly arranged in a viscous solvent. In what the molecules’ attachment to polymers is concerned we consider two different situations : (a) each polymer chain contains at its opposite ends a donor and an acceptor molecule, (b) the donor molecules are dispersed randomly in the solvent and all acceptors are attached to polymers, In both cases we derive the donors’ decay forms exactly.