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We calculate precise numerical values for the nondivergent direct or staggered zero-temperature susceptibilities of the one-dimensional, S=1/2, transverse Ising model at the critical field and for the isotropic XY model in zero field which have not been previously determined analytically. Our method is based on a rigorous approach to calculate dynamic correlation functions for these models. We also investigate the exact nature of the divergenices in the q-dependent susceptibilities. Our results are compared with existing predictions of approximate analytic approaches and numerical finite-chain calculations. Our result for the XY case is directly relevant for the interpretation of recent susceptibility measurements on the quasi-one-dimensional magnetic compound Cs2CoCl4.