This paper explores an automated approach to map one phoneme set to another, based on the acoustic distances between the individual phonemes. The main goal of this investigation is to be able to use the data of a source language, to train the initial acoustic models of a target language for which very little speech data may be available. To do this, an automatic technique for mapping the phonemes of the two data sets must be found. Using this technique, it would be possible to accelerate the development of a speech recognition system for a new language. In our study, we compare different acoustic distance measures and assess their ability to quantify the acoustic similarity between phonemes. The distance measures that were considered are the Kullback-Leibler measure, the Bhattacharyya distance metric, the Mahalanobis measure, the Euclidean measure, the L2 metric and the Jeffreys-Matusita distance. We tested the distance measures by comparing the cross-database recognition results obtained on phoneme models created from the TIMIT speech corpus and a locally compiled South African SUN Speech database. It was found that by selecting an appropriate distance measure, an automated procedure to map phonemes from the source language to the target language can be applied, with recognition results comparable to a manual mapping process undertaken by a phonetic expert.