In this work we present possibilities of the parallelization of numerical examination and simulation of nonlinear systems, especially creating phase-plane diagrams in parallel. For construction of such diagrams Maple was used because it provides algorithms for solving differential equations and two models for parallelization. These are the Task programming model and the Grid programming model. The paper describes the development, the test and the comparison of the parallel programs created according to the two parallelization models. Even using a simple desktop with low number of processors a relative good speedup with a good efficiency could be achieved in both cases. It was also examined how the problem size affects the speedup and the efficiency.