The author studies the Duffing equation \(\frac{dx^2}{d\xi^2} + h \frac{dx}{d\xi} - x(\kappa - \gamma x^2) = f(\Omega\xi)\) under periodic external excitation with frequency \(\Omega\). A relationship is established between the symmetry of quasistatic solutions and regularity of motions occurring due to the periodic perturbation. The author also presents some results of numerical computations.