A new generalization of Poincares normal form theory to nonautonomous differential equations is applied to the Duffing-van der Pol oscillator under a nonautonomous bounded parametric perturbation. The nonautonomous normal form is calculated for parameter values corresponding to the pitchfork scenario. To accomplish the enormous computational effort the computer algebra program MAPLE is used. The normal form can be used to study nonautonomous bifurcation phenomena.