In this paper, an algorithm for continuous speech recognition systems based on the Multi-Band principle is proposed. This algorithm allows the bands to be asynchronous and has a practical complexity that is very close to the complexity of the classical Viterbi algorithm. The question of whether the bands should be constrained to be synchronous or not is discussed. We show that it is advantageous to let the bands asynchronous, as the increase of complexity, compared to the Viterbi algorithm, is low with our algorithm. Moreover, the accuracy must be at least as good as when the bands are synchronous, and, more importantly, different models than phones, can be used in the bands. In this paper, an algorithm for continuous speech recognition systems based on the Multi-Band principle is proposed. This algorithm allows the bands to be asynchronous and has a practical complexity that is very close to the complexity of the classical Viterbi algorithm. The question of whether the bands should be constrained to be synchronous or not is discussed. We show that it is advantageous to let the bands asynchronous, as the increase of complexity, compared to the Viterbi algorithm, is low with our algorithm. Moreover, the accuracy must be at least as good as when the bands are synchronous, and, more importantly, different models than phones, can be used in the bands.