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We calculate the zero-temperature q-dependent susceptibilities of the one-dimensional, S=1/2, transverse Ising model at the critical magnetic field and of the isotropic XY model in zero field which have not been previously determined. Our method, which is based on a rigorous method of calculating dynamic correlation functions for these models, provides precise numerical values for the susceptibilities at wave numbers q=kπ/M for integral M and odd integral k, as well as exact analytic results for the dominant singularities at q=0 and q=π.