The mechanical and thermodynamic stabilities of M 4 AlC 3 (M=V, Nb and Ta) and Ti 4 AlN 3 polymorphs were investigated by means of the first-principles pseudopotential total energy method. All compounds satisfied the Born criteria for mechanical stability, but had different thermodynamic stabilities. Only Ta 4 AlC 3 showed a possible polymorphic phase transformation driven by thermodynamic competition. The present theoretical results support the polymorphism of Ta 4 AlC 3 in experimental synthesis and explain the underlying thermodynamic mechanism. Polymorphism was excluded from V 4 AlC 3 , Nb 4 AlC 3 and Ti 4 AlN 3 .