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(in English) A graph is a two-terminal series-parallel graph if (1) consists of two vertices and an edge between them or (2) is generated by the following two operations:( operation) connecting a pair of two-terminal series-parallel graphs in series, and ( operation) connecting a pair of two-terminal series-parallel graphs in parallel. In this paper, given a natural number , we show a recurrence formula for obtaining the set of two-terminal series-parallel graphs with edges. Moreover, by using the formula, we develop algorithms for enumerating solutions and outputting a two-terminal series-parallel graph randomly. Both algorithms run in polynomial time and space per solution.