In this paper, the AM-FM modulation model is applied to speech analysis, synthesis and coding. The multiband demodulation pitch tracking algorithm is proposed that produces smooth and accurate fundamental frequency contours. The AM-FM modulation vocoder represents speech as the sum of resonance signals modeled by their amplitude envelope and instantaneous frequency signals. Eficient modeling and coding (at 4.8-9.6 kbits/sec) algorithms are proposed for the amplitude envelope and instantaneous frequency signals. Amplitude and frequency modulations of the speech resonances are shown to be perceptually important for natural speech synthesis.