Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)In this article, under certain conditions, we prove the regularity for the solutions of an AllenCahn phase-field type system obtained as limits of approximate solutions constructed by using a semidiscrete spectral Galerkin method. With the help of this improved regularity, as one compares to previous results, we then derive error estimates for the approximate solutions in terms of the inverse of the eigenvalues of the Laplacian operator. The system under investigation may model the evolution of solidification or melting of certain binary alloys. Copyright (c) 2012 John Wiley & Sons, Ltd.351214061414Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq [307833/2008-9]