In binary systems containing rare-earth elements (M) and transition elements (X) several intermetallic compounds with composition between MX2 and MX5 are formed which, according to their mechanical properties, fall into two groups. The brittle alloys are hexagonal or rhombohedral and belong to the M,+IXs,-~ structure series. This series may be considered to be formed by stacking M2X4 blocks (characteristic of Laves phases) with a varying number of MXs blocks (characteristic of the Haucke phase CaCus). The soft alloys with pronounced cleavage have monoclinic symmetry. They belong to a new M, + 1X5, + 2 structure series which contains a new structure block, M2X7, found in the ZrzNi7 structure. A consideration of the intraplanar translation vectors and of the possible rotations of the M2X7 blocks shows that this structure series has three other subseries apart from the monoclinic Zr2Ni7 subseries, these being hexagonal, trigonal and orthorhombic. Point positions for these hypothetical structures are given together with a ready method of recognizing their presence from precession photographs.