In order to take the advantages of spatial modulation (SM) and support the multiple-access (MA) communications requiring high connectivity, we integrate the SM with DS-CDMA to propose a SM/DS-CDMA scheme, which is in favor of attaining both antenna diversity and frequency diversity. Associated with the SM/DS-CDMA scheme, a range of linear and nonlinear multiuser detectors (MUDs) are proposed and studied. Specifically, for linear MUDs, both minimum mean-square-error-aided joint spatial demodulation (MMSE-JSD) and MMSE-aided separate spatial demodulation (MMSE-SSD) are introduced. For nonlinear MUDs, we first present the joint maximum-likelihood MUD (JML-MUD) for demonstrating the potential of the SM-/DS-CDMA systems. Then, the MMSE-relied iterative interference cancellation (MMSE-IIC) is suggested, and the associated two types of low-complexity high-efficiency reliability measurement schemes are proposed. In this paper, we mathematically analyze both the single-user average bit error rate (ABER) of the SM/DS-CDMA systems employing joint spatial demodulation (JSD) and the approximate ABER of the SM/DS-CDMA systems employing the MMSE-JSD. We investigate and compare the ABER performance of the SM/DS-CDMA systems with various detection schemes and also with some legacy schemes. Our studies and performance results show that the SM/DS-CDMA systems in conjunction with appropriate MUD schemes are capable of providing a desirable tradeoff among the number of users supportable, implementation complexity, and the ABER performance.