We study general continuity properties for an increasing family of Banach spaces S-W(P) of classes for pseudo-differential symbols, where S-W(infinity) = S-w was introduced by J. Sjostrand in 1993. We prove that the operators in Op(S-W(P)) are Schattenvon Neumann operators of order p on L-2. We prove also that Op(S-w(p))Op(S-w(r)) subset of Op(S-w(r)) and S-w(p) . S-w(q) subset of S-w(r) provided 1/p+1q = 1/r. If instead 1/p + 1/q = 1+1/r, then S-w(p) w* S-w(q) subset of S-w(r). By modifying the definition of the S-w(p) -spaces, one also obtains symbol classes related to the S(m, g) spaces.