In the field of airborne earth observation there is a special interest in lightweight, low cost imaging radars of high resolution. Such radar systems could play an essential role in small-scale earth observation applications such as the monitoring of dikes, watercourses or areas in which gas pipes or electrical power lines are buried. In order to be successful, such systems should consume little power and they should be small enough to be mounted on very small airborne platforms. Moreover, in order to be of interest to the civil market, cost effectiveness is mandatory. The novel combination of compact frequency modulated continuous wave (FM-CW) radar technology and high resolution synthetic aperture radar (SAR) processing techniques should pave the way for the development of such a small and cost effective imaging radar. Although SAR techniques have already been successfully applied to coherent pulse radars, the practicability of FM-CW SAR is not evident. In pulse SAR signal processing it is assumed that the radar platform is stationary throughout the transmission of a pulse and the reception of the corresponding echo. This so-called stop-and-go approximation is valid since the transmitted pulses are very short. FM-CW radars transmit relatively long sweeps which is why the stop-and-go approximation may no longer be valid. In that case, the change of range during the transmission of a sweep and the reception of the corresponding echo should be taken into account. The effect of the continuous platform motion is investigated by deriving the response of an FM-CW SAR system to a single stationary point target. This investigation shows that the platform motion induces a Doppler frequency shift throughout the SAR observation time. A modification to the range migration compensation is proposed to compensate the Doppler frequency shift at the same time.