As a supplement to the Kryloff and Bogoliuboff method of determining amplitude of oscillation in quasilinear systems, a method based upon energy balance is presented. From the energy balance condition, a criterion for stability of oscillation is deduced for the case of one degree of freedom. The treatment is then generalized to systems of n degrees of freedom, and the n stability criteria are derived in terms of rates of change, with respect to amplitude, of the power supplied and dissipated in the n oscillations