The thesis of the proposed research is that connectionist networks are adequate models for the problem of acoustic phonetic speech recognition by computer. Adequacy is defined as suitably high recognition performance on a representative set of speech recognition problems. Seven acoustic phonetic problems are selected and discussed in relation to a physiological theory of phonetics. It is argued that the selected tasks are sufficiently representative and difficult to constitute a reasonable test of adequacy. A connectionist network is a fine-grained parallel distributed processing configuration, in which simple processing elements are interconnected by scalar links. A connectionist network model for speech recognition has been defined called the temporal flow model. The model incorporates link propagation delay and internal feedback to express temporal relationships. The model is contrasted with other connectionist models in which time is represented explicitly by separate processing elements for each time sample. It has been shown previously that temporal flow models can be 'trained' to perform successfully some speech recognition tasks. A method of 'learning' using techniques of numerical nonlinear optimization has been demonstrated. Methods for extending these results to the problems selected for this research are presented.