Inverse synthetic aperture radar (ISAR) is a well-known technique for obtaining high-resolution radar images. ISAR techniques have been successfully applied in the recent past in combination with pulsed coherent radar. In order to be more appealing to both civilian and military fields, imaging sensors are required to be low cost, low powered, and compact. Coherent pulsed radars do not account for these requirements as much as frequency modulated continuous wave (FMCW) radars. However, FMCW radars transmit a linear frequency modulated (LFM) sweep in a relatively long time interval when compared with the pulse length of a coherent pulse radar. During such an interval the assumption of stop&go is no longer valid, that is the target cannot be considered stationary during the acquisition of the entire sweep echo. Therefore, the target motion within the sweep must be taken into account. Such a problem is formulated and solved for ISAR systems, where the target is noncooperative and additional unknowns are added to the signal model. In the present work, the authors define a complete FMCW-ISAR received signal model, propose an ISAR image formation technique suitable for FMCW radar and derive the point spread function (PSF) of the imaging system. Finally, the proposed FMCW ISAR autofocusing algorithm is tested on simulated and real data.