A new approach to the NMR relaxation theory for a system of magnetic spheres (sufficiently big spherical molecules) is presented. In this paper the NMR spin–lattice relaxation time T1 and spin–spin relaxation time T2 are calculated for nuclear spins I→j, taking into account intermolecular dipole–dipole interactions between the spins I→j, and spins S→k in the magnetic spheres. By an expansion of the dipole–dipole interaction in a series of spherical harmonics, it is possible to separate spatial variables of the interacting spins in a laboratory frame. A simultaneous effect of isotropic rotational and translation diffusion of the spins and relaxation rate of spins S→k is also taken into account.