This paper is concerned with capacities of directsequence (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-tointerference power spectral density ratio. The optimal received power is derived to cause the least interference to other signals while maintaining the acceptable bit energy-to-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. Index Terms-Capacity, DS-CDMA, multicode system, optimal received power, variable processing gain. I. INTRODUCTION F UTURE wireless systems such as FPLMTS/IMT-2000 [1], [2] and UMTS [3] are required to support multirate services (voice, video, data, etc.) with different quality of services (QoS's) [bit error rate (BER), delay, etc.]. Code division multiple access (CDMA) is a promising technique to comply with the above requirements [4]-[6]. It has many attractive features such as high-spectrum efficiency, soft handover, soft capacity, and low-frequency reuse factor [7], [8]. Two approaches have been proposed for supporting multirate services in direct-sequence (DS)-CDMA systems [4], [9]. One is a single-code transmission scheme using a variable processing gain which is defined as the ratio of chip rate to user information bit rate [10]. With the single-code transmission scheme, each user terminal transmits its signal on only one CDMA channel with a processing gain that varies inversely proportional to the user information bit rate. The other is a multicode transmission scheme [11]-[14]. With the multicode transmission scheme, a high-rate data stream is first split into several fixed low-rate streams. The multiple data streams are spread by different short codes with the same chip rate and are added together. Multiple short codes for one high-rate call should be orthogonal over an information bit interval to Manuscript