In this work, we investigated the performance of the coupled-trajectory methods CTMQC and (C)CTTSH in simulating the photodynamics of DMABN and fulvene in full dimensionality using parametrized LVC Hamiltonians for the electronic structure. DMABN and fulvene, together with ethylene, were introduced as "molecular Tully models" aiming to propose to the community prototypical molecular systems to test and to benchmark NAMD algorithms, as their dynamics is reminiscent of the original one-dimensional Tully models . In order to focus solely on the fine details of the dynamics generated based on coupled-trajectory schemes, also in comparison with independent-trajectory methods as MTE and TSH-ED, we treat the electronic structure of DMABN and fulvene analytically using LVC models .