The RCuZn, RAgZn and RAgAl intermetallic compounds (R = rare earth metals) were synthesized and structurally studied by powder and single crystal X-ray diffraction. Among the 28 examined phases, YbAgAl crystallizes in the MgZn2 structure type, while all the others belong to the CeCu2 type. The usual decrease of the cell parameters from lanthanum to erbium is observed, and the clear positive deviation of the three ytterbium compounds can be imputed to Yb divalency. The application of the structural map method to the RMX compounds, where M and X are elements of the 10 to 15 groups, allows some predictions about unknown phases to be proposed.