Using the Langmuir-Blodgett (LB) technique, a poly(paraphenyleneethynylene) (PPE) fluorescent conjugated polymer was assembled on either a quartz substrate (system I) or on the surface of silver nanocube (AgNC) monolayers (system II). The fluorescence intensity of the polymer was studied in system I as a function of the surface density of the polymer sample when deposited on quartz substrates and in system II on the surface coverage of the underlying AgNC monolayers. In system I, a continual increase in the fluorescence intensity is observed as the surface density of excited polymer is increased. In system II, the fluorescence intensity of the polymer first increased until a threshold surface coverage of AgNC was reached, after which it decreased rapidly with increasing surface coverage in the AgNC monolayer. The exciting light intensity dependence is studied before and after this threshold in system II. The results suggest that one-photon processes were responsible for the increased intensity before the threshold, and two-photon processes were responsible for the rapid decrease in the polymer fluorescence intensity after the threshold. These observations are explained by the increase of the surface plasmon enhancement of the exciting light intensity as the nanoparticle surface coverage is increased. In turn, this increases the polymer absorption rate, which results in a continuous increase in the exciton density and is evident by an increase in the fluorescence intensity. At the threshold, the increased exciton density leads to an increase in the rate of exciton-exciton collisions, which leads to exciton-exciton annihilations. When this phenomenon becomes faster than the rate of fluorescence emission, an intensity decrease is observed. By exploiting the surface plasmon enhancement of absorption processes, we have observed the first exciton-exciton annihilation using a low-intensity Hg-lamp continuous wave source.