The proliferation of wireless communications services combined with the limited spectrum availability have placed the bandwidth utilization as a major performance measure. Consequently, the bandwidth allocation technique to multiple signals and the bandwidth occupied by each signal are issues of paramount importance. For voice and bursty data communications, code-division multiple-access provides excellent bandwidth management. The objective to produce constant-envelope signals with compact spectral characteristics is most effectively accomplished using continuous phase modulation. The purpose of this study is to examine detection issues for signals that combine the above techniques. For a synchronous system, the reliable operation of a single-user receiver without power control requires spreading codes that exhibit minimal mutual interference. Signal memory is essential for good performance and precludes the existence of orthogonal codes. Code design is examined for two signal formats that offer different spectral and error rate characteristics. A recursive algorithm that provides the structure and maximum number of codes is presented for both signal formats. Moreover, the code performance is evaluated for an asynchronous system with power control. To avoid the performance limitations of the single-user receiver in the presence of interference and the disadvantages of power control, multiuser detectors are considered for both synchronous and asynchronous systems. The optimum coherent multiuser detector is briefly analyzed and its computational complexity is shown to be prohibitively large for practical applications. For this reason, the emphasis is placed on suboptimum detectors with linear complexity and near-optimum performance. The choice of an appropriate set of decision statistics is crucial for this objective and conventional detectors, if applicable, perform poorly. Two linear complexity detection methods that can be applied to both signal formats are proposed for each system. The individual code design to optimize the error rate for a specific receiver complexity is determined and substantial gains are achieved over antipodal signaling. Moreover, the spectral and error rate performance are largely independent and impressive capacity improvements are obtained over conventional systems for a modest increase in the complexity of the receiver.