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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). (C) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.