Commensurate states, investigated by magnetization, are observed in very pure RBa₂Cu₃O₇(R=Y, Nd) single crystals if the intervortex distance a_c becomes equal to an integer number k of the crystal lattice constant (na_c = kd). Incommensurate states at higher temperatures and fields develop, split up and become finally commensurate with k / 2or even with a smaller fraction k/n of the crystal lattice constant (na_c = kd). These additional states of higher order (n > 1) are related to a superstructure of the vortex lattice with respect to the crystal lattice.