Hands-free communications between cellular phones must be robust enough to withstand echo-path variation, and highly nonlinear echoes must be suppressed at low cost, when acoustic echo cancellation or suppression is applied to them. This paper proposes a spectrum-selective nonlinear echo suppression (SS-ES) approach as a solution to these issues. SS-ES is characterized by the selection of either a spectrum of the residual signal from an adaptive filter or a spectrum of the sending input signal depending on the amount of linear echo cancellation in an adaptive filter. Compared to conventional methods, the objective evaluation results of the SS-ES approach show an improvement of approximately 0.8-2.2dB, 0.23-2.39dB, and 0.26-0.50 in average echo return loss enhancement (ERLE), average root-mean-square log-spectral distortion (RMS-LSD), and the perceptual evaluation of speech quality (PESQ) value, respectively, under echo-path variation and double-talk conditions.