In　this　paper,　we　introduce　the　notion　of　generalized　multiresolution　structure　(GMS)　in　the　setting　of　reducing　subspaces　of　L-2(R-d).　For　a　general　expansive　matrix,　we　obtain　a　necessary　and　sufficient　condition　for　GMS,　and　prove　the　existence　of　GMS　in　a　reducing　subspace.　Using　GMS,　we　obtain　a　pyramid　decomposition　and　a　frame-like　expansion　for　signals　in　reducing　subspaces.