A first study on Hakka and mixed Hakka-Mandarin speech recognition (SR) is reported in this paper. The main focus of the study is on solving the problem of the lack of a large text corpus for training a reliable language model. In the Hakka SR, several methods to use the information of part of speech and Hakka-Chinese word translation to assist in language modeling are proposed. For mixed language SR, a method to train a mixed Hakka-Mandarin acoustic model is suggested. Experimental results show that the proposed language and acoustic modeling approaches are promising for Hakka and mixed Hakka-Mandarin SR.