This paper analyses the maser oscillator equations which describe the interaction between the resonant cavity and the inverted population of the electron spin system of the paramagnetic substance. It is shown that these equations will not allow periodic solutions thus refuting the theory, based on computer solutions, that this interaction is responsible for the pulsed mode of operation of the oscillator.Characteristics of solutions of these equations are determined analytically, and the ambiguity of computer solutions is discussed with the aid of examples. Numerical solutions are presented which show that periodic solutions may be induced by supplementing the spin system equation with an additional term.