Foreign accented speech recognition systems have to deal with the acoustic realization of sounds produced by non-native speakers that does not always match with native speech models. As the standard native speech modeling alone is generally not adequate, it is usually extended with models of phonemes estimated from speech data of foreign languages, and often complemented with extra pronunciation variants. In this paper, the focus is set on the speech recognition of multiple non-native accents. The speech corpus used was recorded from speakers originated from 24 different countries. The introduction of models of phonemes of the target language adapted on foreign speech data is presented and detailed. For the recognition of non-native speech comprising multiple foreign accents, this approach provides better performance than the introduction of standard foreign units. The selection of the most frequent acoustic variants for each phoneme is also discussed as this method makes recognition results more homogenous across speaker language groups. Furthermore, the adaptation of the acoustic models on non-native speech data is studied. Results show that detailed models, which include the modeling of extra pronunciation variants through acoustic units estimated on foreign data, benefit more from the task and accent adaptation process than baseline standard models used for native speech recognition. In addition, experiments show that an adaptation of the acoustic models on a limited set of foreign accents provides speech recognition performance improvements even on foreign accents absent from the adaptation data.