Abstract: Correctness is a key attribute of software trustworthiness. Abstractly, software correctness can be represented as whether or not the implementation of software satisfies its specification. However, in the real world, it is difficult to get the satisfaction absolutely. In the course of developing and designing software, implementation is often modified in order to satisfy its specification. This means that the software is more and more close to correctness, i.e. software correctness is a dynamic course. In order to describe the dynamic correctness of software, in this paper, the abstract characterization and the limit theory of dynamic correctness based on parameterized bisimulation are proposed. Firstly, the infinite evolution mechanism of parameterized bisimulation is established. Parameterized limit bisimulation is defined in order to characterize the relation between a series of software implementations obtained in the real design and its specification, and some special examples are shown. Secondly, parameterized bisimulation limit is given, and the recursive characterization of parameterized bisimulation limit is stated. Finally, some algebraic properties are proved, such as the uniqueness of parameterized bisimulation limit and the consistence between parameterized bisimulation limit and parameterized bisimulation.