Since the electronic potential energy surfaces drive the nuclear dynamics and the nonadiabatic couplings induce population transfer, the electronic structure crucially affects the outcome of a NAMD simulation, as it a) Electronic mail: peter.schuerger@uni-wuerzburg.de b) Electronic mail: federica.agostini@universite-paris-saclay.fr has been argued recently. Nonetheless, other "parameters" have non-negligible effects on the overall coupled electron-nuclear dynamics after photoexcitation, e.g., the dynamics method used for the propagation of the nuclei, in terms of evolution equations, which will be discussed in this work, and their initialization . In the domain of NAMD, trajectory-based techniques have been very successful since they mimic the quantum-mechanical nuclear evolution using swarms of trajectories that obey classicallike equations of motion . The chemical physics and physical chemistry literature is rich of works presenting original approaches, benchmarking novel methods against more established ones, comparing different flavors of traditional techniques, demonstrating the performance of the most efficient schemes with challenging applications. All these works are of fundamental importance to understand where the methodological developments in the context of NAMD methods stand and where further theoretical or technical developments are required. cus our analyses solely on the nature of the nuclear dynamics, bypassing some numerical or technical difficulties often encountered when using ab-initio/semiempirical electronic-structure methods, such as lack of convergence or time-consuming electronic-structure calculations. Nonetheless, DMABN and fulvene are simulated in full dimensionality, namely using 57 vibrational modes for DMABN and 30 vibrational modes for fulvene, thus we report analyses well beyond the low-dimensional studies performed in previous works on coupled-trajectory methods. In both LVC models, as in the original molecular models, only two electronic states participate in the dynamics, namely the first two singlet excited states, S 1 and S 2 , in DMABN and the lowest two singlets, S 0 and S 1 , in fulvene. DMABN and fulvene show challenging photodynamics since they exemplify the dual-avoided crossing and the extended avoided crossing with reflection typical of the original one-dimensional models proposed by Tully in Ref. [20]. In the former case, multiple transfers of the populations between two electronic states that remain close in energy are affected by the interplay of interferences and recoherences of the nuclear wavepackets that split and recombine in the regions of strong nonadiabatic coupling. In the latter case, the nuclear wavepacket goes through a sloped conical intersection, transferring population from one electronic state to another, but the topology of the intersection is such that, upon reflection, a second passage through the same intersection causes a novel nonadiabatic event.