The effects of vibration on certain electric and magnetic properties of H-2, N-2, HE and CO are reported. These properties include electric field gradients, generalized Sternheimer shielding constants, electric-field-gradient polarizabilities, nuclear shielding constants, and shielding polarizabilities. The calculations were based on both electron correlated and uncorrelated methods. Pure vibrational effects, where appropriate, were investigated as well as conventional vibrational averaging. It is found that in many cases vibration plays a very significant role.