Developing trusted softwares has become an important trend and a natural choice in the development of software technology and applications, and software trustworthiness modeling has become a prerequisite and necessary means. To discuss and explain the basic scientific problems in software trustworthiness and to establish theoretical foundations for software trustworthiness measurement, combining the ideas of dynamical system study, this paper studies evolutionary laws of software trustworthiness and the dynamical mechanism under the effect of various internal and external factors, and proposes dynamical models for software trustworthiness, thus, software trustworthiness can be considered as the statistical characteristics of behaviors of software systems in the dynamical and open environment. By analyzing two simple examples, the paper explains the relationship between the limit evolutionary behaviors of software trustworthiness attributes and dynamical system characteristics, and interprets the dynamical characteristics of software trustworthiness and their evolutionary complexity.software trustworthiness, trustworthiness attributes, evolutionary complexity, dynamical system In the last more than ten years, environments for software running and development have transited from static closeness to dynamical openness. The open changing running environments lead to a variety of uncertainty factors, making it hard to guarantee the correctness, safety and security, reliability, availability and effectiveness of software systems, even their own survivability. In the open changing environments, software systems have become more and more fragile and very hard to trust, and very often not working in the expected way, faults and failures arising, causing incidents even disasters directly or indirectly. Thus, both academic and industry in IT show highly concerns for software trustworthiness and invest into its research issues.Whether or not the services provided by software systems are trustable, particularly in dynamical, open and distributed environments, is a critical problem in safety-crucial applications, for example financial applications, space technology applications. How to guarantee the trustworthiness of