Complex systems (processes) of responsible purpose are becoming more common in the modern world. The responsibility for designing complex systems is due to, for example, circumstances such as dependence on the latest health or even the lives of large numbers of people, the environmental security of regions and high material costs. These include responsible industrial and energy facilities, elements of transport, communication and safety systems, computer systems and networks, equipment for complex medical interventions in the human body, educational institutions, etc. What unites these systems and makes them subjects of research is that their complexity requires the use of modern information technologies and the appropriate "embedded" computer system for obtaining and processing real-time reliable data on the state of the object. Existing embedded information systems, as a rule, should be trained in advance to detect deviations of the parameters of the state of the controlled object from the norm, as well as to calculate and perform (sometimes, with the help of the operator) actions to compensate for such deviations. But, unfortunately, there are other systems that get into a situation (crisis), when their "passport" parameters are subject to significant deviations, and the existing, "built-in" information support for such situations is not trained, and quickly help in overcoming the consequences online crisis is not capable. After all, the controllability of SS SS, the fight against crises that these processes encounter, is based on the available adequate and relatively fast (they must have time to destroy the pseudo-resistant damaged object) models and methods of making urgent anti-crisis decisions in management. The aim of the work is to increase the efficiency of crisis management processes of rapid development of complex multi-parameter organizational and technical systems through the development and implementation of new models and methods. environment or, at least, the preservation of targets in times of crisis. To achieve this goal, the paper analyzes complex systems of responsible purpose in terms of their resistance to damage and crises; classification (sorting) of complex systems of responsible purpose with wandering elements is executed; the general algorithm of the general parametric space accumulation process at management of difficult systems is constructed; the implementation is performed and the practical significance of the obtained results is evaluated.