The exploration of speech processing for endangered languages has substantially increased in the past epoch of time. In this paper, we present the acoustic-phonetic approach for automatic speech recognition (ASR) using monolingual and cross-lingual information with application to under-resourced Indian languages, Punjabi, Nepali and Hindi. The challenging task while developing the ASR was the collection of the acoustic corpus for under-resourced languages. We have described here, in brief, the strategies used for designing the corpus and also highlighted the issues pertaining while collecting data for these languages. The bootstrap GMM-UBM based approach is used, which integrates pronunciation lexicon, language model and acoustic-phonetic model. Mel Frequency Cepstral Coefficients were used for extracting the acoustic signal features for training in monolingual and cross-lingual settings. The experimental result shows the overall performance of ASR for cross-lingual and monolingual. The phone substitution plays a key role in the cross-lingual as well as monolingual recognition. The result obtained by cross-lingual recognition compared with other baseline system and it has been found that the performance of the recognition system is based on phonemic units . The recognition rate of cross-lingual generally declines as compared with the monolingual.