In this paper we develop the frame theory of suaces. We will show that for every Parseval frame of suaces (Wi)i2I for a Hilbert space H, there exists a Hilbert space K _ H and an orthogonal basis of suaces (Ni)i2I for K such that Wi = P(Ni), where P is the orthogonal projection of K onto H. We define an atomic resolution operator for an atomic resolution of the identity, which even yield a reconstruction formula.