Two experiments are described in which frequency selectivity was estimated, in simultaneous and forward masking, for each ear of subjects with moderate (25–60 dB HL) unilateral cochlear hearing losses. In both experiments, the signal level was fixed for a given ear and type of masking (simultaneous or forward), and the masker level was varied to determine threshold, using an adaptive, two‐alternative forced‐choice procedure. In experiment I, the masker was a noise with a spectral notch centered at the signal frequency (either 1.0 or 1.5 kHz); threshold was determined as a function of notch width. Signal levels were chosen so that the noise level required at threshold for a notch width of zero was similar for the normal and impaired ear of each subject in both simultaneous and forward masking. The function relating threshold to notch width had a steeper slope for the normal ear than for the impaired ear of each subject. For the normal ears, these functions were steeper in forward masking than in simultaneous masking. This difference was interpreted as resulting from suppression. For the impaired ears, significant differences in the same direction were observed for three of the five subjects, but the differences were smaller. In experiment II, psychophysical tuning curves (PTCs) were determined in the presence of a fixed notched noise centered at the signal frequency (1.0 kHz). For the normal ears, the PTCs were sharper in forward masking than in simultaneous masking. For the impaired ears, the PTCs were similar in simultaneous and forward masking, but those in forward masking tended to be sharper at masker frequencies far removed from the signal frequency. Overall, the results suggest that suppression is reduced, but not completely absent in cases of moderate cochlear hearing loss.