The time dependent spectral properties of a first and a second generation dendrimer with peryleneimide chromophores at the rim and a terrylenediimide chromophore in the core were investigated by time resolved polychromatic transient absorption measurements. The obtained results of the dendritic structures were compared with those of three model compounds. In the perylene-terryiene dendrimers a very fast energy transfer process was observed. Besides energy transfer singlet-singlet annihilation could be observed. It could be concluded that competition between the rates of energy transfer and of singlet-singlet annihilation is dependent on the dendrimer generation.