In this paper, we describe the use of either words or morphemes as lexical modeling units and the use of either graphemes or phonemes as phonetic modeling units for Arabic automatic speech recognition (ASR). We designed four Arabic ASR systems: two wordbased systems and two morpheme-based systems. Experimental results using these four systems show that they have comparable state-of-the-art performance individually, but the more sophisticated morpheme-based system tends to be the best. However, they seem to complement each other quite well within the ROVER system combination framework to produce substantially-improved combined results.