The effect of the so-called change of picture for operators in approximate relativistic theories on the second-order properties arising from some external perturbation, is considered. By means of the direct perturbation theory the general formula for the lowest-order relativistic correction to second-order properties is derived. The term which arises from the change of picture for the external perturbation operator is identified and evaluated for dipole and quadrupole polarizabilities. For the 1s(1/2) state of the hydrogen-like ions this term is found to bring about 16% and 7% of the total lowest-order irelativistic correction to the dipole and quadrupole polarizabilities, respectively. This finding is discussed in terms of its importance for long range interactions between heavy systems.