Abstract: In this paper, we focus on the convergence mechanism of ε-bisimulation under probabilistic processes to discuss the dynamic correctness of the software. Firstly, ε-limit bisimulation is defined for reflecting the dynamic relation between software specification and implementation. Some special ε-limit bisimulations are showed. Secondly, ε-bisimulation limit is proposed, which states the specification is the limit of implementation under ε-bisimulation. The uniqueness of ε-bisimulation limit and consistence with ε-bisimulation are presented. Finally, the substitutivity laws of ε-bisimulation limit with various combinators are proved.