A simple analytical treatment is developed for the differential equation(d2u/dt2)−&egr;(1−u2)×(du/dt)+u=0(van der Pol), in order to study the behavior of its solution assumed bounded in (0, ∞). It is shown, without any further assumption, that, if &egr;≪1,u(t) can be approximated closely, fort≧0, by a simple oscillation with amplitude 2. This is a more precise form of a statement due to van der Pol. It is further shown thatu2(t)+u′2(t)∼4, t≧0, 0<&egr;≪1. The method and results are then extended to the more general equation(d2u/dt2)−&egr;F(u)(du/dt)+u=0, in particular, forF(u)=1−u4, 1−2au−u2,a=constant, also to the non‐homogeneous equation(d2u/dt2)−&egr;F(u)(du/dt)+u=given function of t. The analytical results obtained in this paper show a remarkable agreement with those obtained for the same equations by mechanical means (on the differential analyzer).