  We present a generalized QCD factorization scheme for the high energy
inclusive polarized process, (A, S_A) + (B, S_B) -> C + X, including all
intrinsic partonic motions. This introduces many non-trivial azimuthal phases
and several new spin and k_T dependent soft functions. The formal expressions
for single and double spin asymmetries are discussed. Numerical results for
A_N[p(transv. polarized) p -> pi + X] are presented.
