This paper deals with the problem of digital demodulation of FM signals transmitted over Rayleigh and Rician fading channels. The Rayleigh and Rician fading channels are represented by two quadrature multiplicative non-zero mean white Gaussian processes in addition to an additive zero-mean white Gaussian noise. Quasi-optimum digital baseband demodulation algorithms using various nonlinear estimation techniques are derived. The digital demodulator structures are then simulated on a digital computer for an FM system with first order message spectrum for various values of the parameters for Rayleigh and Rician channels.