The development of automatic speech recognition systems poses several known difficulties. One of them concerns the recognizer's accuracy when dealing with non-native speakers of a given language. Normally a recognizer precision is lower for non-native users, hence our goal is to improve this low accuracy rate when the speech recognition system is confronted with a foreign accent. A typical usage scenario is to apply these models in applications where European Portuguese is dominant, but where English may also frequently occur. Therefore, several experiments were performed using crossword triphone based models, which were then trained with speech corpora containing European Portuguese native speakers, English native speakers and English spoken by European Portuguese native speakers.