Cyclostationarity is a property of vibration and acoustic signals recorded on rotating machines operating at constant speed. It states that the statistic properties of signals are periodic: the random process defined by the signal observed at a given position in the cycle is stationary, the cycle being defined as the angle interval between two identical configurations of the mechanical system. Cyclostationarity is not fully satisfied if the signals are acquired in the time domain on rotating machines with a fluctuating rotation speed. Indeed, if the instantaneous rotation speed is not purely periodic, it means that time samples taken at a constant time interval (equal to the average cycle duration) do not correspond exactly to an angle in the cycle. In this particular case, a synchronous averaging of cycle realizations can still be processed to estimate a periodic part using a predefined trigger angle to align cycle realizations before the averaging process. In these conditions, the synchronous average depends on the chosen synchronization angle: each point of the synchronous average is an estimate of the expected value of the signal at a given time preceding or following the synchronization angle. The synchronous average can be computed as a function of the synchronization angle, varying over an entire cycle. The result is a moving synchronous average that can be post-processed for diagnosis purposes. For example, a time frequency representation of the moving synchronous average can be computed, and the synchronization angle maximizing each point of the time frequency map can be easily extracted. Under certain conditions of instantaneous speed fluctuations, this analysis allows the precise localization of different mechanical events in the cycle, as well as their contributions in the analyzed vibration or acoustic signal. The analysis of the moving synchronous average leads also to the estimation of the energy loss of the synchronous average processed in angle caused by cycle-to-cycle speed fluctuations.