In this work, we present a complete derivation of the NonAdiabatic Bohmian DYnamics (NABDY) equations of motion. This approach naturally emerges from a transformation of the molecular time-dependent Schrodinger equation in the adiabatic representation of the electronic states. The numerical implementation of the method is discussed while simple nonadiabatic models are employed to address the accuracy of NABDY and to reveal its ability to capture nuclear quantum effects that are missed in trajectory surface hopping (TSH) due to the independent trajectory approximation. A careful comparison of the correlated, NABDY, and the uncorrelated, TSH, propagation is also given together with a description of the main approximations and assumptions underlying the "derivation" of a nonadiabatic molecular dynamics scheme based on classical trajectories. (C) 2013 AIP Publishing LLC.