The inverse synthetic aperture radar (ISAR) uses the Doppler effect caused by the rotation and translation of the target to improve the cross-range resolution. Usually, these two motions have not been distinguished and have been processed in one dimension in the cross-range compression of the ISAR. In this paper, it is shown that Doppler components caused by these two motions can be separated, so that two-dimensional cross-range compression by elevation compression due to rotation and azimuth compression due to translation is possible for a target such as a boat that moves slowly in translation with rolling. Further, the boundary condition is derived that enables image reconstruction from the Doppler effect caused by the two motions, rotational and translational. For radar parameters such as the transmission wavelength lambda, the resolution Delta of the ISAR image, and the range D to be visualized, two-dimensional cross-range compression becomes possible if the relationships alpha > lambda/4 pi Delta, nu less than or equal to lambda R-0/2T(0)D hold for target parameters such as the maximum rolling angle alpha, rolling period T-0, translation speed nu, and relative distance R-0 from the radar. By computer simulation, an image reconstruction example using the two-dimensional cross-range compression algorithm is presented. (C) 1999 Scripta Technica, Electron Comm Jpn Pt 1, 82(9): 10-18, 1999.