The performance of modern communications transmitters utilising multi-carrier modulation techniques is highly sensitive to non-linear distortions arising mainly from the high-power amplifier. 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 known as memory effects. This study presents analytical expressions that can be used to evaluate the impact of the distortions induced by time-varying non-linearities with memory on the bit error rate performance of a multi-carrier signal such as the orthogonal frequency division multiplexing. The timevarying non-linearity with memory is modelled by a time-varying Volterra series. The resulting mathematical expressions are applied to specific situations, allowing for a quantitative evaluation of the system performance degradation. & The Institution of Engineering and Technology 2015.