This paper describes an analytic method of determining the region of transient stability in state space for a synchronous generator. The boundary of the region of stability is found in the form of a power series; the coefficients appearing in the series are determined recursively by consideration of conditions at the unstable singular point of the system. A variation of the basic method is also described, in which an approximate solution is initially assumed for the stability boundary anda power series is used as a correction term. Results are given for the case of a variable damping coefficient, and also for the case of a machine with velocity governor. Very good accuracy for critical clearing times is achieved with only a small amount of computation.