A system is a frame in a Hilbert space if there are positive constants and such that for all . A system is a fusion frame or a frame of subspaces if
where is the orthogonal projection onto the subspace . One of the main results of this paper is a proof that the dual fusion frame (with the frame operator given by ) is indeed a fusion frame. Other results deal with alternate duals, i.e., systems so that , and frame operators for a pair of two Bessel fusion sequences (where only the upper bound above is required to hold).