In this talk we consider a class of parametric perturbed ordinary differential equations with a generalized $\Phi$-Laplacian type term. We will show how topological methods and suitable connectivity arguments can be used to obtain global bifurcation of nontrivial periodic solutions having the same period as that of the perturbation term and emanating from the set of stationary solutions. We will also illustrate possible extensions of the previous results to delay differential equations.