Perturbed Hamiltonian systems of the type \(\dot x=f(x)+\epsilon g(x,t,\lambda)\) are considered, where \(f: {\mathbb{R}}^ 3\to {\mathbb{R}}^ 2\), \(g: {\mathbb{R}}^{4+k}\to {\mathbb{R}}^ 3\) are sufficiently smooth, g(x,t,\(\lambda)\) is periodic in t, \(\lambda\) is a k-vector parameter, and \(\epsilon\) is a small positive parameter. Existence and bifurcation theorems for homoclinic orbits are obtained. The perturbations may or may not depend explicitly on time. In particular, the existence of bifurcation values \(\lambda_ 0\) is proved under suitable hypotheses, for \(\epsilon >0\) sufficiently small, at which quadratic homoclinic tangencies or (nontransverse) homoclinic orbits occur. Applications are made to a periodically forced Duffing equation with weak feedback.