Let 2 be a variety of algebras with involution * over a field of characteristic zero and cn(V, *) the corresponding sequence of *-codimensions. Here,we characterize those varieties V such that cn (V, *) is polynomially bounded. We prove that V is such a variety if and only if G2,M V, where G2 and M are two explicit finite-dimensional algebras with involution previously constructed. It follows that G2 and M generate the only two varieties of algebras with involution with almost polynomial growth and there is no variety with intermediate growth.