A noncoherent, bandwidth-efficient modulation scheme is proposed for frequency-hopping multiple-access (FH-MA) networks. The proposed scheme is a combination of noncoherent M-ary amplitude-shift keying (NMASK) and orthogonal frequency-division multiplexing (OFDM). Using this scheme will minimize the required data bandwidth. The number of frequency. slots available to the users will increase significantly for a fixed spread-spectrum bandwidth (BWSS). The effect of the multiple-access interference will be reduced. Simple and accurate bit error rate expressions have been derived for FH-OFDM-MASK in additive white Gaussian noise channels and for FH-OFDM-ASK in Rayleigh fading channels.