In　practice,　the　time　variable　cannot　be　negative.　The　square　integrable　function　space　L-2(R+)　defined　on　the　half　real　line　R+　=　(0,　8)　models　the　causal　signal　space.　Given　a　＞　1,　this　paper　addresses　F-a-frames　in　the　setting　of　subspaces　of　L-2(R+).　We　establish　the　connection　between　subspace　F-a-frames　and　orthogonal　projections;　characterize　all　bounded　linear　operators　on　L-2(Z　x　T-a)　that　transform　F-a-frames　into　other　F-a-frames　for　a　subspace　V　of　L-2(R+);　and　obtain　some　sufficient　conditions　for　constructing　F-a-frames　for　V　from　an　arbitrarily　given　one.