This paper presents morpheme-based language models developed for Amharic (a morphologically rich Semitic language) and their application to a speech recognition task. A substantial reduction in the out of vocabulary rate has been observed as a result of using subwords or morphemes. Thus a severe problem of morphologically rich languages has been addressed. Moreover, lower perplexity values have been obtained with morpheme-based language models than with word-based models. However, when comparing the quality based on the probability assigned to the test sets, word-based models seem to fare better. We have studied the utility of morpheme-based language models in speech recognition systems and found that the performance of a relatively small vocabulary (5k) speech recognition system improved significantly as a result of using morphemes as language modeling and dictionary units. However, as the size of the vocabulary increases (20k or more) the morpheme-based systems suffer from acoustic confusability and did not achieve a significant improvement over a word-based system with an equivalent vocabulary size even with the use of higher order (quadrogram) n-gram language models.