Forward masking of sinusoidal frequency modulation (FM) was measured with three types of maskers: FM, amplitude modulation (AM), and a masker created by combining the magnitude spectrum of an FM tone with random component phases. For the signal FM rates used (5, 20, and 40 Hz), an FM masker raised detection thresholds in terms of frequency deviation by a factor of about 5 relative to without a masker. The AM masker produced a much smaller effect, suggesting that FM-to-AM conversion did not contribute substantially to the FM forward masking. The modulation depth of an FM masker had a nonmonotonic effect, with maximal masking observed at an intermediate value within the range of possible depths, while the random-phase FM masker produced less masking, arguing against a spectrally-based explanation for FM forward masking. Broad FM-rate selectivity for forward masking was observed for both 4-kHz and 500-Hz carriers. Thresholds measured as a function of the masker-signal delay showed slow recovery from FM forward masking, with residual masking for delays up to 500 ms. The FM forward-masking effect resembles that observed for AM [Wojtczak and Viemeister (2005). J. Acoust. Soc. Am. 188, 3198-3210] and may reflect modulation-rate selective neural adaptation to FM.