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Transient probability prblems were studied in four three-state power system and one seven state telecommunication system. The study was carried out using the Adams Method and another method which is developed for this study. The new method is named as Stabilization Method (SM). The new method is compared with Adams method from stability and accuracy view points. It was found that the SM method required less programing effort compared to the Adams method. The accuracy of stabilization method (SM) compares well with Adams when sufficiently small time interval is chosen. The relationship between the CPU time and the number of states was found to be non-linear for the SM method.