A simple model Hamiltonian is analyzed within the framework of time-dependent perturbation theory to show how nuclear vibrations induce instantaneous electromagnetic moments in the electron cloud of a molecule. These moments can be rationalized in terms of nuclear electromagnetic shielding tensors. The vibrational motion of a nucleus also gives rise to induced electric and magnetic fields at the other nuclei. This effect is discussed introducing nuclear electric and magnetic coupling tensors, which are related to nuclear shieldings and other molecular properties. Nuclear electromagnetic couplings have been calculated for water, ammonia and methane molecules using the random-phase approximation.