In this thesis we developed the time-dependent version of the multicomponent density functional approach to treat time-dependent electron-nuclear systems. The method enables to describe the electron-nuclear coupling fully quantum mechanically. No Born-Oppenheimer approximation is involved in the approach. The multicomponent density functional theory is formulated for an electron-nuclear system in the body-fixed coordinate frame attached to the nuclei. It allows us to describe properly the internal properties of the system.