The past two decades have witnessed a rapid expansion of the telecommunications industry. This growth has been primarily fuelled by the proliferation of the digital communication systems and services which have become easily available through wired and wireless networks. Current research trends involving integration and packetisation of voice, video and data channels into true multimedia communications, promise a similar technological revolution in the next decade. The available bandwidth in wire based terrestrial network is a relatively cheap and expandable resource. However in satellite and cellular radio systems the bandwidth is inherently limited and an expensive resource. In order to accommodate ever growing numbers of subscribers whilst maintaining high quality and low operational costs, it is essential to maximise the spectral efficiency. The research presented in this thesis has focused on the development of new source compression algorithms, tailored for human speech in order to improve the spectral efficiency of digital transmission systems. Recently there is an increasing interest on speech coding algorithms which combine various existing technologies in order to improve the speech quality .whilst maintaining the low transmission rate of the existing coding techniques. The aim of the research presented in this thesis was to develop a complete hybrid coding algorithm which combines harmonic and waveform approximating coding techniques. In order to integrate the two coding paradigms novel phase synchronisation and classification techniques were developed. The perceptual quality of the speech synthesised using the unquantised hybrid model achieves nearly transparent quality. The hybrid model was used to develop variable bit rate coders, which are particularly advantageous for voice storage, Code Division Multiple Access (CDMA) wireless networks, packet switched networks, and statistical multiplexing of speech for multi channel communications.