The processing of synthetic aperture radar (SAR) echoes collected during radar antenna beam steering, such as in the staring spotlight, sliding spotlight, and TOPS operating modes, requires additional efforts due to the limited pulse repetition frequency (PRF). Subaperture processing is mostly used in these cases, but the complexity arising from subaperture dividing and recombination is preferably avoided. The two-step approach (TSA) is an elegant solution to full-aperture processing. Nevertheless, for high-resolution airborne and spaceborne SAR processing, the TSA is still faced with a number of difficulties, which does not occur, however, in subaperture processing. For instance, the high range bandwidth induces Doppler spectrum aliasing during the spectral analysis (SPECAN) stage of the original TSA. Moreover, the Doppler spectrum obtained in TSA, when inverse Fourier transformed back to the slow time domain, might also suffer from aliasing, which precludes the estimation and correction of the unknown residual motion error or tropospheric disturbance. In this article, we extend the TSA to address these problems and present a full-aperture processing framework to precisely focus the high-resolution airborne and spaceborne SAR data. Simulation of X-band spaceborne SAR echoes with transmission signal bandwidth of 3.6 GHz and coherent integration angle of 12.5° has validated the extended TSA (ETSA). Meanwhile, experimental X-band airborne SAR data with the same range and azimuth resolution are also processed using the ETSA, where the conventional autofocusing techniques have been smoothly incorporated.