In a previous paper1expressions were obtained for the distortion of the modulation when a frequency-modulated wave passes through network whose group-delay and amplitude characteristics both exhibit small departures from constancy. An ideal discriminator network has the property that when it is fed with a frequency-modulated wave the amplitude modulation of the output is an exact copy (except for scale factor) of the frequency modulation of the input. This can be achieved by a network whose group-delay characteristic is constant and whose amplitude characteristic is linear. In the present paper the theory given in the previous paper is extended to cover discriminator networks whose characteristics exhibit small departures from these ideal forms. Single-tone and noise-band modulations are considered. Two numerical examples are given, one being a design of 2-tuned-circuit discriminator, which is considered in relation to a 240-channel f.d.m. telephony system, and the other is an improved balanced discriminator suitable for a 600-channel system.