Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. The definition of multiple pseudofames for subspaces with real number translation is proposed. The notion of a generalized multiresolution structure (GMS) of is also introduced. The pyramid decomposition scheme is derived based on a GMS. As a major new constribution the sufficient condition for the existence of multiple pseudoframes for subspaces is derived based on such a GMS.