The work presents time-resolved polychromatic transient absorption measurements for two generations of pyrene-terrylene dendrimers and was compared with those of three model compounds. The chemicals and solvents were of A.R. grade and used as such. As a solvent for all samples toluene (HPLC, Aldrich) was used without further purification. From the study it can be said that if there are multiple excitations within a molecule there will be most probably a competition between different kinetic processes. It seems that in T1P´4 and in T2P´8 there is a competition between the annihilation process and the energy transfer process. The outcome of this competition cannot be determined quantitatively since this will depend on the conformation of the molecule. A small difference could be related to the relative amount of donor acceptor chromophores and/or to the relative amount of energy transfer rate/singlet-singlet annihilation rates which can change by increasing the generation number.