This thesis examines the acoustic-modeling problem in automatic speech recognition from an information-theoretic point of view. This problem is to design a speech-recognition system which can extract from the speech waveform as much information as possible about the corresponding word sequence. The information extraction process is broken down into two steps: a signal processing step which converts a speech waveform into a sequence of information bearing acoustic feature vectors, and a step which models such a sequence. This thesis is primarily concerned with the use of hidden Markov models to model sequences of feature vectors which lie in a continuous space such as R sub N. It explores the trade-off between packing a lot of information into such sequences and being able to model them accurately. The difficulty of developing accurate models of continuous parameter sequences is addressed by investigating a method of parameter estimation which is specifically designed to cope with inaccurate modeling assumptions.