The security of Grid-systems assumes the consistency, accessibility and confidentiality of system and user information resources that circulate within those systems. These characteristics can be obtained by applying modern tools and technologies from network perimeter security as used in corporate information systems. Our goals are to provide: (i) validity and consistency of computational processes and their results (protection from Grid-terrorism); (ii) protection from interception or substitution for user routines and their results within the Grid (protection from Grid-spying); (iii) protection from full and partial unauthorized usage of computational resources (protection from Grid-parasites). As Gridsystems gain in importance as strategic information systems, reaching the above goals requires the development of an appropriate security policy. This policy should guarantee high immunity against various threats within the Grid-system environment. This paper presents an approach for creating advanced tools and technologies for strengthening security in Grid-systems. This approach is based on the principles of proactivity and self-similarity of distributed security management systems.