We present the first results obtained by proton ((1)H) nuclear magnetic relaxation studies of molecular dynamics in a supermolecular liquid-crystal dendrimer exhibiting columnar rectangular and smectic-A phases. The (1)H spin-lattice relaxation time (T(1)) dispersions are interpreted using two relaxation mechanisms associated with collective motions and local molecular reorientations of the dendritic segments in the low- and high-frequency ranges, respectively. The T(1) values show a drop around 2.3 MHz that is attributed to a contribution coming from cross-relaxation between (1)H and nitrogen nuclear spins. In the high-frequency range the motions appear to be of similar nature in both mesophases and are ascribed to reorientations of dendritic segments (belonging to the core and/or to the mesogenic units) characterized by two correlation times. Notable differences in the dynamics between the columnar and layered phases are observed in the low-frequency range. Depending on the mesophase they are discussed in terms of elastic deformations of the columns and layer undulations. In this study we find that the dendritic core influences the dynamics of the mesogenic units both for local and collective motions. These results can be understood in terms of spatial constraints imposed by the dendritic architecture and by the supermolecular arrangement in the mesophases.