The diffusion coefficients of 1-palmitoyl-2-(pyrenodecanoyl)-sn-glycero-3-phosphocholine (pyr10PC) in different bilayer membranes are determined from global analysis of the time-resolved fluorescence of the pyrene monomer and excimer emissions. The global kinetic model involves a time-dependent reaction rate coefficient derived from the analytical solution of the diffusion equation for bimolecular reactions in the two-dimensional surface of the membrane. The bilayer membranes are single unilamellar vesicles (SUV's or liposomes) composed of dioleoylphosphatidylcholine (DOPC), 1-stearoyl-2-arachidonoylphosphatidylcholine (SAPC), or dipalmitoylphosphatidylcholine (DPPC). All SUV's except the one composed of DPPC are in the liquid crystalline state. Liposomes composed of mixtures of DOPC and SAPC in various molar ratios are also investigated by the pyrene excimer reaction. The diffusion constant becomes larger when the fraction of SAPC in the mixed bilayers increases, indicating an apparent increase in fluidity. The latter observation is supported by photostationary measurements of the pyrene excimer to monomer intensity ratios of the same liposomes.