Despite the advantage of high average power output, traditional continuous transmission FM (CTFM) sonars suffer from two major defects: separate transmit and receive transducers are required, and the demodulated signal is unavailable for a proportion of the sweep period. The paper shows how, by using a dual-demodulation system, the demodulated signal can be made continuous, resulting in the complete elimination of the blind time and in a range resolution as good as two wavelengths of the mean frequency. Experimental results using a CTFM air sonar justify both these claims.