Data obtained with coherent HF backscatter radars of the Super Dual Auroral Radar Network (SuperDARN) are routinely analyzed with a standard algorithm based upon the simplifying assumption that the backscattered signal consists of a single source, characterized by its Doppler velocity and spectral width. More complex situations are often encountered where the signal includes several sources, either due to the additional existence of ground scatter or due to multiple ionospheric lines, related to a strongly inhomogeneous velocity field. We analyze the response of the standard algorithm to such signals and we propose to use high-resolution spectral analysis methods, namely, the multiple signal classification (MUSIC) method, to separate multiple echoes with different velocity and spectral width. We analyze theoretically the autocorrelation function of the received signal, and we show that its structure satisfies the criteria for processing by the MUSIC algorithm. A statistical numerical simulation of SuperDARN data processing by the MUSIC method allows us to evaluate the performances and the limits of applicability of the method. We show and illustrate with examples taken from experimental data that the main improvements are (1) the correct separation of mixed echoes from ground and ionosphere, which enhances the quality of ionospheric convection measurements, and (2) the capability to resolve multiple ionospheric sources which appear in regions of inhomogeneous convection. These multiple sources can be used to resolve small-scale structures in the velocity field. ¿ 1998 American Geophysical Union