Abstract Digital speech communication in increasingly heterogeneous communication networks requires exible speech coding algorithms. In Voice-over-IP (VoIP), for example, signicant parameters such as the instantaneous bit rate, the delay or the packet loss rate may heavily vary over time. Hierarchical speech coding algorithms are particularly well suited to accommodate to these changing conditions, as bit rate reductions can be eected at any point along the communication network without transmitting any additional signaling information. The objective of this thesis is hierarchical vector quantization (HVQ) and its application to speech coding. The aim is to increase the exibility of variable bit rate (VBR) speech coding algorithms while maintaining the coding eciency in a rate-distortion sense. The concept of HVQ is based on a decomposition of the input vector into subvectors that comprise a hierarchical representation of the input vector. Each subvector is quantized separately by using individual VQ resulting in corresponding blocks or packets of bits. These packets form a xed-rate hierarchically structured bit stream from which reduced-rate bit streams can be extracted simply by dropping packets, whereas least crucial packets are discarded rst. A general HVQ scheme is developed that comprises well-known generic approaches to hierarchical coding such as multistage VQ and multiresolution VQ. The formulation of a general approach to hierarchical coding within the VQ framework allows us to apply the theoretical tools provided by rate-distortion theory and high-rate theory in order to analyze the performance penalty that those generic hierarchical coding systems suer compared to non-hierarchical coding systems. Based on the insight gained from this theoretical performance analysis, new bit rate ecient algorithms for hierarchical speech coding are developed.