In this paper, we analyze an asynchronous multiple-chip-rate DS/CDMA system, in which signals are transmitted at different chip rates, processing gains, carrier frequencies, and transmission powers, according to their own bit rates and bit error rates. We define the partial correlation function for the chip waveforms and derive the multiple access interference of the system. The average bit error probability for the system is evaluated by means of the Gaussian approximation, The effects of the chip rate and processing gain upon the system performance are investigated.