With increasing size of sequence databases heuristic search approaches have become necessary. Hidden Markov models are the best performing search methods known today with respect to discriminative power, but are too time complex to be practical when searching in large sequence databases. In this report, heuristic algorithms that reduce the search space before searching with traditional search algorithms of hidden Markov models are presented and experimentally validated. The results of the validation show that the heuristic search algorithms will speed up the searches without decreasing their discriminative power.