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Multicode-code division multiple access (CDMA) supports a variety of transmission rates within a wireless network. However, providing packet-delay guarantees in a multicode-CDMA network is difficult because its transmission capacity is time varying even in an error-free wireless channel. In this paper, we develop a packet-scheduling algorithm called multicode-deficit round robin (DRR) as a solution to the problem. The basic idea of multicode-DRR is to separate the time-varying capacity into a deterministic component and a variable component, and to use these components to serve time-sensitive and non-time-sensitive traffic, respectively. With the proposed scheduling algorithm, simulation results have confirmed that the maximum packet delays for time-sensitive traffic never exceed their target upper bounds.