This paper deals with the theoretical study of the magnetorhelogical properties of dilute suspensions of polymer coils with ferromagnetic nanoparticles adsorbed on the macromolecules. The analysis shows that, under an applied magnetic field, these coils elongate in the field direction and swell. Both these factors lead to a significant increase in the effective viscosity of the system. Estimates show that in the magnetopolymer compositions, strong magnetoviscous effects are expected even though in standard ferrofluids these effects are negligible.