  Recently introduced time-dependent renormalized-natural orbital theory
(TDRNOT) is extended towards a multi-component approach in order to describe
H$_2^+$ beyond the Born-Oppenheimer approximation. Two kinds of natural
orbitals, describing the electronic and the nuclear degrees of freedom are
introduced, and the exact equations of motion for them are derived. The theory
is benchmarked by comparing numerically exact results of the time-dependent
Schr\"odinger equation for a H$_2^+$ model system with the corresponding TDRNOT
predictions. Ground state properties, linear response spectra, fragmentation,
and high-order harmonic generation are investigated.
