Resonant motions of systems of mutually gravitating rigid bodies are investigated with the help of the periodic and condltionally periodic solutions for multifreguency nonlinear systems, containing a small parameter. The conditions of existence have been obtained for the periodic solutions of these systems in the principal cases as well as in some degenerate ones. The existence has been proved of the periodic solutions of three kinds In the unrestricted problem of three rigid bodies, possessing quasiconcentric distributions of densities. With the help of the periodic solutions of the first kind of this problem, a posslble explanation has been given to the observed resonance In the Venus´ motlon. Perlodlc solutions have been found In the planetary version of the problem of η + 1 rigid bodies, generalizlng the corresponding periodic solutions of the problem of η + 1 point bodies. It is supposed that the bodies of the system have small dimensions and quasiconcentric distributions of densities.