This paper presents the new approach to the analysis and synthesis of a parallel-processing architecture. The novelty of the procedure lies in the generalized space–time system of co-ordinates and the space–time transformation of sets in the system. The parallel space–time computing structures (PASTICS) are introduced, main principles are presented and the functional structure of processing unit is analyzed. Computing in the PASTICS is considered as a minimization of a certain potential function which can be derived from the state-transition and output functions, corresponding to the problem to be solved. The problem of synchronization of different processing units must be solved similarly as it is done in the data-flow control computers. Two important cases of application of the PASTICS are mentioned.