This paper discusses the performance of asynchronous direct-sequence spread-spectrum multiple-access systems using binary or quaternary phase-shift keyed signals with the strict bandwidth-limitation by Nyquist filtering. The signal-to-noise plus interference ratio (SNIR) at the output from the correlation receiver is derived analytically taking the cross-correlation characteristics of spreading sequences into account, and also an approximated SNIR of a simple form is presented for the systems employing Gold sequences. Based on the analyzed result of SNIR, bit error rate performance and spectral efficiency are also estimated.