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The symbol error probability (SEP) performance of time-hopping (TH) ultra-wideband (UWB) systems in the presence of multiuser interference (MUI) and timing jitter is considered without making the usual Gaussian approximation (GA). Contrary to previous studies restricted to binary modulation formats, we analyze and evaluate the performance of such multiuser TH-UWB systems employing M-ary pulse position modulation (PPM) and a correlation receiver. Using the Gaussian quadrature rules (GQR) method and by considering the correlator outputs to be statistically independent, a semi-analytical method for the SEP evaluation is proposed. Furthermore, by modeling the timing jitter as a Gaussian process, we study the degradation it causes on the overall system performance (SEP and capacity). The accuracy of the proposed approach has been verified by means of computer simulations. Furthermore, a comparison with equivalent performance results obtained using the GA has provided precise conditions where this approximation should not be used.