This article discusses methods to support assurance of surveillance monitoring; and compliance verification knowledge management (CV-KM). The discussion includes aspects of primary monitoring systems; the different environments in which they operate; the verification problem solving and decision making tasks; the problem structure and the coordination of the review process to facilitate truth maintenance. Based on the ALCOD prototype developed with the Surveillance Division of the Australian Stock Exchange, the surveillance operation is considered a primary monitoring function with the analysis of the resulting output the secondary monitoring function - the assurance component. Keywords Supporting compliance monitoring assurance, Primary surveillance systems (PSS), Compliance verification, Simple environments, Complex environments, Suspected non-compliance event (SNCE), Secondary monitoring.