Abstract. In this talk I will show that two simply-connected spaces of finite type are rationally equivalent if and only if their singular cochains considered as associative algebras can be connected to each other by a zig-zag of quasi-isomorphisms of associative algebras. This result is a consequence of the more general statement that two commutative algebras can be connected by a zig-zag of quasi-isomorphisms of commutative algebras if and only if they can be connected by a zig-zag of quasi-isomorphisms of associative algebras. This is joint work with Ricardo Campos, Dan Petersen and Daniel Robert-Nicoud.