This paper describes the theory of stochastic transduction and our current implementation for English text-to-phoneme conversion. A transduction grammar is defined which generates orthographic-phonemic word pairs; here the sentential derivation is modelled as a Markov process. We envisage that our grammar, which is regular, will ultimately operate at three levels: morphemic, syllabic and phonographic. Thus far, we have only implemented the phonographic grammar. The most likely translation is obtained by an extended form of the Viterbi algorithm with probabilities inferred by the Viterbi update procedure. Testing with 4676 words yields a word translation accuracy of around 82% but generalisation to unseen words remains to be tested.