Commensurability effects between vortex distance and crystal lattice constant are investigated by angular dependent magnetization in very pure twinned and twin-free NdBa₂Cu₃O_y single crystals. With increasing temperature the incommensurate states split up and become finally commensurate with half the crystal unit cell. These additional  commensurate states are related to a second intrinsic pinning potential within the unit cell or alternatively to a superstructure from distortion of the vortex lattice with respect to the crystal lattice. The role of twins which favor and/or stabilizes the double  periodicity is discussed furthermore.