We investigate the monotonicity of the minimal period of the periodic solutions of some quasilinear differential equations involving the p-Laplace operator. The monotonicity is obtained as a function of a Hamiltonian energy in two cases. We first extend to the case p≥2 classical results for p=2 due to Chow and Wang, and Chicone. Then we consider a differential equation associated with a fundamental interpolation inequality in Sobolev spaces. In that case, we generalize to p≥2 a recent result due to Benguria, Depassier and~Loss when p=2.