Quasisynchronous (QS) Code Division Multiple Access (CDMA) is currently being considered for a variety of wireless applications and services because QS-CDMA enables information transmission with a good quality of service. In this paper, for M-ary signaling, the Symbol Error Rate (SER) performance of QS-CDMA communication system with a maximal ratio combiner (MRC) over frequency-selective, time-nonselective multipath Generalized Gamma (GG3) fading channels is derived not only for any deterministic spreading sequences but also for any chip-limited chip waveforms, and it is investigated for Rectangular, Half-Sine, and Raised-Cosine chip waveforms by means of numerical and simulation results. Numerical and simulation results show that the performance of QS-CDMA is as good as or slightly better than synchronous CDMA (S-CDMA) when the maximum quasisynchronous delays do not need to be less than some specific values depending on the path power scattering. With this flexibility of quasisynchronous delays, both the transmitter and receiver complexities are reduced as quasisynchronous communication is a challenging task for researchers. Additionally, since not only the spreading sequences but also the partial autocorrelation functions of the chip waveform are influential on the performance of multipath QS-CDMA, a measure, Partial Power Ratio (PPR) is defined based on these partial autocorrelation functions in order to select or design a chip waveform for quasisynchronous communication. Furthermore, results show that QS-CDMA using the chip waveform whose PPR is greater has better performance.