The kinetics of compaction of hot-pressed materials in the TiN - AlN system has been studied. The shrinkage of TiN - AlN composites (for an AlN concentration varying within 10 – 90 vol.%) occurs within 10 – 15 min in the temperature range 1750 – 1850°C at a pressure of 65 MPa. The calculated activation energy for hot-pressed ceramic [50% TiN + 50% AlN] was found to be 5.0 eV, intermediate between the activation energies for neat TiN and AlN species. This implies that the sintering of hot-pressed heterophase mixtures characterized by a decrease of temperature under isothermal conditions is an activated process.