This paper is concerned with capacities of direct-sequence (DS) code-division multiple-access (CDMA) systems accommodating multiclass services with different transmission rates and bit error rates (BER's). The capacities are expressed by inequalities to which the number of accepted calls of each class should conform. Those inequalities are necessary and sufficient conditions satisfying the requirement of the bit energy-to-interference power spectral density ratio. The optimal received power is derived to cause the least interference to other signals while maintaining the acceptable bit energy-ta-interference power spectral density ratio. It is shown that if the maximally receivable power of a call of each class is identical in the multicode system and the single-code system using a variable processing gain, the capacities of both systems are also identical in nonfading channels. However, in multipath fading channels, the multicode system is shown to be better than the single-code system in terms of capacity, Capacity is also derived in a dynamic multiple-cell environment.