In the article two types of the speculative methods: the speculative method with a fixed integration step and the speculative method with a variable integration step will be presented. These methods are an original approach to the trasient states analysis appearing in the physical and electrical systems, in which the transient state is described by a large system of ordinary differential equations, linear or nonlinear. A general idea of these methods is based on decomposition of the total time of transient analysis into subintervals in which computations are conducted in parallel. The application of speculative methods allows to reduce the time of computations in relation to commonly used sequential algorithms. As the example of the application of speculative methods, the analysis of transient state described by a system of 10 differential equations will be presented.