Multiresolution　analysis　(MRA)　and　frame　multiresolution　analysis　(FMRA)　in　L2(ℝ)　play　a　significant　role　in　the　construction　of　wavelets　and　frame　wavelets　for　L2(ℝ).　In　this　paper,　the　notions　of　MRA　and　FMRA　in　a　reducing　subspace　of　L2(ℝ)　are　introduced,　from　which　the　construction　of　wavelets　and　frame　wavelets　for　this　subspace　is　obtained.　Many　examples　are　also　provided　to　illustrate　the　general　theory.　In　particular,　most　of　them　are　about　the　space　with　its　frequency　lying　in　[0,　∞),　which　is　closely　related　to　various　Paley-Wiener　Theorems.