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An analytical investigation is carried out to evaluate the impact of cross phase modulation due to non-linear Kerr effect in a single mode fiber on the transmission performance of an optical CDMA system. Expression for the intensity modulation (IM) induced by PM-IM (phase modulation-intensity modulation) conversion due to GVD (group velocity dispersion) is derived and the mean and variance of MAI (multiple access interference) at the output of SIK (sequence inversed keyed) correlator receiver is determined. Performance results are evaluated in terms of BER (bit error rate) performances of OCDMA system with variable probe power, fiber length, number of users, bit rate and code length considering 31 chip and 127 chip m-sequence codes. Results show that the system performance deteriorates significantly due to the IM caused by GVD and PM.