Abstract By a theorem of G. Birkhoff, every algebra in an equationally defined class of algebras K is a subdirect product of subdirectly irreducible algebras of K . In this paper we show that this result is true for any class of structures. not necessarily algebraic, closed under isomorphisms and direct limits. Quasivarieties in the sense of Malcev are examples of such classes of structures. This includes Birkhoffs result as a particular case.