The photophysical properties and the excitation energy transfer (EET) process of a series of first generation dendrimers having a rigid tetrahedral core and different numbers of peryleneimide chromophores at the rim were investigated by steady-state and time-resolved fluorescence spectroscopy in toluene. It was shown that the model dendrimer containing only one chromophore decays monoexponentially with a time constant of 4.2 ns. In the multichromophoric compounds an additional long decay time of 7.4 ns assigned to an "excimer-like" state was observed, and its contribution increases with the number of chromophores. The time-resolved polarization measurements resulted in a nanosecond relaxation component due to the rotation of the entire dendritic structure. However, for the compounds having more than one chromophore, an additional fast anisotropy decay time of 100-200 ps was observed which corresponds to Forster type EET among the chromophores.