A theory for studying nonlinear dynamics of molecular liquids is developed. The theory is based on the extension of the time-dependent density functional theory to a rigid interaction-site model. From the theory, one can calculate time changes in interactionsite densities using molecular parameters such as the inertial moment of a molecule. The theory has a differential and integral basic equation with a kernel function, which is not included in the time-dependent density functional theory of simple liquids. The application of the theory to diatomic and three-site molecules allows one to obtain explicit expressions of kernel functions.