A Langmuir-type film balance equipped with a fluorescence microscope for the near ultraviolet and a spectrometer for time-resolved fluorescence spectroscopic studies (suited for lifetimes greater than or equal to 5 ns) was built. The aim was to study membrane dynamics of diffusion-controlled bimolecular reactions in two-dimensional fluids. Complete exclusion of molecular oxygen was achieved. Under this condition, the dynamics of excimer formation may be studied for probe concentrations as small as 0.5 mol%. At the same concentration, domain formation due to lateral phase separation may be visually observed. In the first part, the time evolution of the fluorescence of monomer and excimer in monolayers of L-alpha-dimyristoylphosphatidylcholine (DMPC) is studied. A pyrene-labeled lecithin serves as an excimer-forming probe. Probe concentration and lateral packing density of the lipids are varied. A method is developed by which the fluorescence lifetime of the monomer and the lateral diffusion coefficients are obtained with high accuracy (lifetime better than 7.5%, diffusion coefficient better than 15%) from the decay of the monomer fluorescence. The method is based on the analysis of the excimer formation in terms of the Smoluchowski theory modified for two-dimensional fluids. It is shown that the time course of the excimer formation is determined by a strongly time dependent rate of association k(t). The strong time dependence is a consequence of the fact that there is no stationary solution of the diffusion equation in two-dimensional fluids. The time evolution of the excimer fluorescence is analyzed in a model of so-called "pseudo-excitation". In the application part the variation of lateral diffusivity with lipid packing density is studied. It is shown that it agrees only in the small packing density regime with the predictions of the free volume model. Over the whole range of packing densities investigated here, the viscosity of the monolayer shows an exponential dependence on density, as was predicted for ordinary fluids by Frenkel. Finally, the method is applied to mixtures of DMPC with cholesterol. A phase diagram for high cholesterol concentrations is established. It is shown that by careful analysis of excimer formation dynamics it is possible to detect local phase separation in cases where the classical methods (thermodynamical and fluorescence microscopy) fail. A remarkable influence of a few percent of pyrene-labeled phospholipids on the phase boundaries is established.