The performance of modern communications transmitters utilizing multi-carrier modulation techniques is highly sensitive to non-linear distortions arising mainly from the highpower amplifier (HPA). The increase in symbol duration makes the system more sensitive to time-varying channels. In addition, the wideband characteristics of multi-carrier signals result in frequency-dependent distortions, typically know as memory effects. This paper presents analytical expressions that could be used to evaluate the impact of the distortions induced by time-varying non-linearities with memory on the BER performance of a multi-carrier signal such as the orthogonal frequency division multiplexing (OFDM). The time-varying non-linearity with memory is modeled by a time-varying Volterra Series. The resulting mathematical expressions are applied to an specific situation, allowing for a quantitative evaluation of the system performance degradation.