The components of large digital systems structured as toroidal grids are tested and diagnosed in three stages. At the first stage, the components of the subsystems as specified by the primary layout are checked in parallel. At the following two stages, the subsystems obtained from the primary subsystems by one-step right (downward) shift are checked in parallel as well. For the large digital systems, a multiagent organization of system diagnosis was developed. The functional characteristics and interrelations of the seven types of agents required for realization of the test and diagnosis components of the large digital systems under consideration were determined. An example of the multiagent organization of diagnosis of the components of a nine-module toroidal subsystem was considered.