The problems of designing real-time computing systems are considered. Models and methods for the realization of tasks for performing complex work are proposed. This is the basis for the development of mathematical support for real-time systems. The developed tools allow solving the problems of compiling an admissible schedule for the execution of processes, synchronizing computations, dynamic memory allocation, etc. We present new algorithms for constructing an admissible (a) uniprocessor schedule with interruptions in the presence of precedence relations between jobs are presented; (b) multiprocessor schedule with interrupts at given directive intervals without precedence relations; (c) multi-processor schedule, taking into account the costs of processing interrupts and switches