  Under conditions of Levinson-Smith type, we prove the existence of a
$\tau$-periodic solution for the perturbed generalized Li\'enard equation
u''+\phi(u,u')u'+\psi(u)=\epsilon\omega(\frac{t}{\tau},u,u') with periodic
forcing term. Also we deduce sufficient condition for existence of a periodic
solution for the equation u''+\sum_{k=0}^{2s+1}
p_k(u){u'}^k=\epsilon\omega(\frac{t}{\tau},u,u'). Our method can be applied
also to the equation
u''+[u^2+(u+u')^2-1]u'+u=\epsilon\omega(\frac{t}{\tau},u,u'). The results
obtained are illustrated with numerical examples.
