Synthetic aperture radar (SAR) processors generally assume that the scene reflectors are stationary over the time of integration of the image. When this is not the case, various kinds of image distortions may occur, such as target displacement or smearing. In the present paper, oscillating targets are considered. It is shown that such targets are smeared in azimuth to an extent determined by the amplitude and frequency of the oscillation. The reason may be stated in terms of the slow-time Doppler shift of the target. The Doppler shift is not constant, but varies with aperture time. We show that time-frequency analysis provides useful tools to handle problems of this kind. The choice of analysis method is often difficult. Here, we compare several methods of the Cohen's class, and show good results with the data adaptive optimal kernel method. This method, being adaptive, dispenses with some of the trial-and-error often necessary with quadratic methods. We show data from a controlled experiment where oscillating reflectors were placed within a scene imaged by an airborne SAR system. The reflectors are smeared in azimuth. We estimate the amplitude and frequency of the oscillations from the time-frequency distributions.