Several adaptive algorithms for robust echo cancellation use nonlinear reference and/or error functions. Most of them require time-variant threshold estimators, e.g., noise level estimators or double-talk detectors, since their nonlinearities have to be adjusted in response to changes in near-end noise or speech signal levels. We propose a new frequency domain adaptive algorithm: the gradient-limited fast least-mean-squares (GL-FLMS), in which the coefficients are updated by using a nonlinear function of the error scaled by the reference magnitude, i.e., the error-to-reference ratio (ERR). When the acoustic coupling level between loudspeaker and microphone is bounded, the ERR is also bounded in the case of single-talk, but may increase during double-talk. The GL-FLMS limits unexpected increases in the ERR with fixed thresholds and prevents divergence of the coefficients, while not neglecting updates to adjust when a large reference signal introduces a large error during single-talk.