The developed theory of the orientational mobility of individual segments of a perfectly branched dendrimer is used to calculate the relaxation spectrum of a dendrimer. Frequency dependences of NMR relaxation 1/T1 and of the nuclear Overhauser effect have been theoretically calculated from the Brownian dynamics simulation data. The dendrimer segmental orientational mobility is governed by three main relaxation processes: (i) the rotation of the dendrimer as a whole, (ii) the rotation of the dendrimer's branch originated from a given segment, and (iii) the local reorientation of the segment. The internal orientational mobility of an individual dendrimer segment depends only on the topological distance between this segment and the terminal shell of the dendrimer. Characteristic relaxation times of all processes and their contributions to the segmental mobility have been calculated. The influence of the number of generations and the number of the generation shell on the relaxation times has been studied. The correlation between the characteristic times and the calculated relaxation spectrum of the dendrimer has been established.