We study the molecular orientational vibrations (MOVs), using analytical method, in Langmuir (Langmuir-Blodgett) monolayers. At the present stage of our study, we fix the hydrophilic heads of the amphiphilic molecules and model the hydrophobic alkane chains as rigid rods. We have considered different tilt orders in our study and self-consistently determined the tilt angle at various surface pressures and temperatures. The study of these MOVs leads us to a breakthrough in the analytical theory for monolayers, with which we are enabled to analytically investigate a wide range of thermodynamical properties, such as angular correlation functions and specific heat, and to calculate structural functions in scattering experiments. As to MOV itself, a universal frequency gap at k=0 exists (except at the upright-tilted phase transition point). This frequency gap is closely related to the upright-tilted phase transition as we explain in the text. Comparison of our results with those from previous Monte Carlo simulations is made and shows good agreement.