This thesis studies the Bowen resonance fluorescence mechanism of OIII in three planetary nebulae: NGC 6210, 7027, and 7662. It utilizes the best spectra to date of this phenomena in the wavelength range of 3100 A-3850 A. The data are presented in the form of flux ratios relative to the strong 3444.1 A line and compared to expectations based on current theory. Harrington's theoretical predictions which take into account the additional enhancement of some of the Bowen resonance fluorescence lines due to pumping of next higher energy level, OIII 2p3d \sp3P\sbsp10, show agreement with NGC 7027 and 7662; however, predictions by Neufeld agree poorly for all three planetary nebulae studied. Enhancement by charge exchange reactions is quite evident in NGC 6210. Finally, the HeII 3203 A line is used to determine efficiencies of 0.57 and 0.48 for NGC 7027 and 7662 respectively, only slightly higher than Kallman and McCray's prediction of 0.42; while NGC 6210 yielded an impossible value of 1.37.