A data-flow program net is a graph representation of data-flow programs consisting of three types of nodes, AND-node, OR-node and SWITCH-node, which represent arithmetic/logical, data merge and context switch operations respectively. Token self-cleanness is an important property of a data-flow program and is such that if date-flow programs satisfy the property then a date-flow computer can efficiently withdraw copies from given programs during executions. In this paper, we classify program nets into SWITCH-less, OR-less and general nets, and analyse structures of data-flow program nets to propose verification methods of token self-cleanness by investigating token numbers appearing on the edges. As a result, a necessary and sufficient condition is proposed for SWITCH-less data-flow program nets and sufficient conditions are given for OR-less and general data-flow program nets.