Poincaré's small-parameter method and the Krylov-Bogoliubov asymptotic method are among the number of basic methods used for the study of nonlinear oscillations. Poincaré's method was developed in conformity with stationary (periodic) oscillations [1], although it may be extended to nonstationary oscillations as well (see, for example, [2]). The Krylov-Bogoliubov method may be used, first of all, for a study of nonstationary oscillations, but it is, of course, completely applicable to periodic oscillations as well [3], It is sometimes asserted that these methods are different in principle. Thus, for example, Polncaré's method requires the convergence of series in a small parameter which represent periodic solutions. On the other hand, in the description of the Krylov-Bogoliubov method it is emphasized that the question of the convergence of small-parameter expansions does not arise at all and that in some cases these series are known to be divergent. It is pointed out that the expansions used serve only for the construction of asymptotic approximations of any desired degree of accuracy under the condition that the small parameter approaches zero. In the present paper we consider the periodic solutions of quasilinear systems with one degree of freedom, and the calculations are shown only for self-contained systems. A comparison is made between the first few terms of expansions obtained by the two methods.