The aim of this work is to investigate the methods of representation and calculation of the stability of multi-machine power-systems. Two aspects of the problem are particularly considered: the modelling of rotating machinery and the solution method for the ordinary differential equations. The results obtained from site tests are compared with results obtained using a range of machine representations. The accuracy of the models is thus judged, some refinements made and other deficiencies indicated. Methods of improving the efficiency of the trapezoidal method and Zakian's method for the solution of the system differential equations are investigated. For comparative purposes the Backward Euler and Runge-Kutta- Gill methods are also studied, and other means of obtaining a step by step solution discussed. It is concluded that at present the trapezoidal method is the most satisfactory but it has limited potential for further development.