Effects of light intensity on the steady-state fluorescence quenching kinetics are examined for general cases where the bimolecular quenching can occur via long-range energy transfer processes and the potential of mean force between the energy donor and acceptor molecules is not negligible. Approximate analytic expressions are derived for the steady-state quenching rate constant and for the ratio of the steady-state intensity of unquenched to quenched fluorescence. The analytic results are compared with the exact results obtained from numerical analysis and the results of conventional theories.