An analytical formulation of the outage probability in terms of bit error rate specification for variable bit rate (VBR) multiclass services in a multi-code direct-sequence ultra-wideband (DS-UWB) system with Rayleigh monocycles is derived via an outage probability analysis. The analytical framework is formulated for the general case in which different traffic classes have different varying bit rates. Multiple spreading codes are used by each user to achieve variable bit rate (VBR). Closed-form expressions for the signal at the correlator's output during a frame interval and the power of the interference resulting from one of the active spreading codes from the interfering users on one pulse are explicitly derived for Rayleigh monocycles. The analytical work leads to the determination of the capacity region of a multi-code DS-UWB system supporting VBR services. Numerical results of the capacity region are also presented.