In speech recognition, accomplishing high accuracy recognition and real time recognition is an important objective. Recently, large vocabulary continuous recognition systems have been developed, yet an accurate and efficient search algorithm is needed that can get an optimum candidate without matching all possible paths. In this paper, the evaluation of recognition performance utilizing the beam search and the A[sup *] search method will be described. Although the beam search does not guarantee an optimum result, it is rare that an optimum result cannot be gotten if use is made of suitable beamwidth and pruning threshold, and then the search can operate quickly because of reduced search space. In experiments on both isolated spoken word recognition and continuous speech recognition, the beam search method was superior to the A[sup *] search for recognition accuracy and speed. In addition, from the fact that there exists an optimum path in the region of the beamwidth in almost all cases, we propose an A[sup *] search method with beamwidth constraints.