A convolutionally coded M-ary orthogonal direct sequence code division multiple access (DS-CDMA) system in time-varying frequency-selective Rayleigh fading channels is considered in this work. We propose several novel soft demodulation algorithms based on interference cancellation and suppression techniques that can be coupled with soft decoding to improve the system performance in an iterative manner. The performance of the proposed demodulation algorithms is evaluated numerically and proved to achieve substantial bit error rate (BER) performance gain compared with the conventional detection schemes.