The approximate analysis of nonlinear flutter problems by the method of KrylofT and BogoliubofT is outlined. The method is presented in a simple fashion based upon the concept of "harmonic balance." Because of the nature of the response of flutter systems to sinusoidal excitations of various frequencies, it appears that the method should be particularly suitable in the present application. A nonlinear system is reduced to an equivalent linear system, of which some of the parameters become functions of the amplitudes of motion. The flutter behavior of nonlinear systems can thus be explained, often very simply, in terms of the knowledge of the linear system. A few examples of wing-control surface flutter with nonlinear structural stiffnesses, solved by an analog computer by Woolston, et al.,. are re-examined. The analytical results predict, at least qualitatively, the behavior as described there. I t is difficult to compare the flutter boundaries of the present analysis and the published analog results because of the use of different amplitude parameters. The agreement is good in one case where comparison is possible. The method is next applied to the finite amplitude flutter of buckled panels in a supersonic stream, first studied by Fung with a two-mode representation, to illustrate its capability in handling cases with many degrees of freedom. Without using the mode approach, it is shown that the nonlinear behavior may be deduced from a knowledge of the linear system, which in this particular case becomes identical to a problem treated by Hedgepeth.