A treatment of nuclear vibrational motions in two-photon absorption is laid out in detail. Perturbation theory is used to develop working formulas for diatomic molecules and tested for the X (1)Sigma(+)-A (1)Pi transition of carbon monoxide. The results are compared with the exact numerical values. Certain vibrational contributions, not previously recognized, are found to make an important contribution to the two-photon absorption probability.