This paper presents and analysis the common existing sequential pattern mining algorithms. It presents a classifying study of sequential pattern-mining algorithms into five extensive classes. First, on the basis of Apriori-based algorithm, second on Breadth First Search-based strategy, third on Depth First Search strategy, fourth on sequential closed-pattern algorithm and five on the basis of incremental pattern mining algorithms. At the end, a comparative analysis is done on the basis of important key features supported by various algorithms. This study gives an enhancement in the understanding of the approaches of sequential pattern mining.