The dissipative dynamics of excitons in the outer antenna system of photosynthetic bacteria is investigated using an equation of motion approach. The coupling to environmental degrees of freedom is treated employing Redfield relaxation theory. It is shown that within the secular approximation the concept of essential excitonic states provides a convenient means for reducing the number of coupled differential equations to be solved. Further we derive the appropriate quenching matrix that accounts for the now of excitation energy between weakly interacting pigment pools, Numerical simulations are presented to emphasize the influence of the various relaxation and dephasing mechanisms as well as the excitonic band structure on the energy transfer.