By NMR and static and dynamic light scattering we investigated how the micelle size, shape, and aggregation number vary during the solubilization of triolein in mixed aqueous solutions of the nonionic surfactant C12En (n ) 5 or 6) and the nonionic triblock copolymer Synperonic L61 (SL61). The latter was found to strongly accelerate the solubilization, although the copolymer alone is unable to solubilize triglycerides. A series of solutions containing different concentrations of surfactant and copolymer has been studied. The light scattering shows that we are dealing with giant micellar aggregates, each of them containing hundreds to thousands of surfactant molecules and dozens of copolymer molecules. Assuming that the micelles have the shape of prolate ellipsoids, we calculated their length and width. The results indicate that the initial, strongly elongated micelles transform into spherical or slightly ellipsoidal ones at the end of solubilization. The micelle aggregation number and hydrodynamic radius decrease by factors of 2-6 during the solubilization; i.e., one empty micelle splits into several smaller swollen micelles of radius 4-5 nm. The NMR measurements reveal that the equilibrium solubilization capacity (solubilized oil/mol of surfactant) is virtually not affected by the addition of SL61. Hence, the copolymer accelerates the process without influencing its final result; that is, SL61 acts as a promoter of solubilization. The results are used in the subsequent two papers of this series to develop a kinetic model of triglyceride solubilization and to verify it against experimental data.