Nuclear quantum dynamics beyond the Born-Oppenheimer approximation is performed using quantum trajectories. Withintheadiabaticrepresentationoftheelectronicstates, NABDY(NonAdiabaticBohmianDYnamics) is used in combination with DFT and LR-TDDFT to perform on-the-fly nonadiabatic quantum dynamics. Simple numerical test systems and current limitations of the method are discussed.