A new computer code SPECOMP has been developed to calculate displacement damage for compound materials. The code uses primary recoil atom energy distributions from the SPECTER code and thus requires no access to nuclear data bases. For each combination of recoil and matrix atom, the code determines the secondary displacement functions and integrates over the recoil energy distributions. The net displacements for a compound are then the weighted sum of these results for all combinations of atoms in the compound. Calculations have been completed for fusion tritium breeders, insulators, and alloys. In cases where there are large mass differences between atoms in the compound, the damage calculated by SPECOMP is significantly different than the weighted sum of elemental damage from SPECTER. Displacement functions for various materials are being added to the SPECTER package for routine use, and SPECTER users can easily perform calculations for new compounds.