In a Hilbert space {Hilbert space}, discrete families of vectors {hj} with the property that f = ΣJ hJ for every f in {Hilbert space} are considered. This expansion formula is obviously true if the family is an orthonorma1 basis of {Hilbert space}, but also can hold in situations where the hj are not mutually orthogonal and are "overcomplete." The two classes of examples studied here are (i) appropriate sets of Weyl-Heisenberg coherent states, based on certain (non-Gaussian) fiducial vectors, and (ii) analogous families of affine coherent states. It is believed, that such "quasiorthogonal expansions" will be a useful tool in many areas of theoretical physics and applied mathematics.