Results are presented for the osmotic pressure of concentrated aqueous micellar surfactant solutions. Using a pressure-nulled membrane osmometer, we measure the osmotic pressure of solutions of the cationic surfactant, cetylpyridinium chloride (CPC), and the anionic surfactant, sodium dodecyl sulfate (SDS), in 0.01 M sodium chloride. Nanofiltration membranes serve as the semipermeable barrier and permit measurement of large osmotic pressures over volume fractions that span the micellar region ranging from just above the critical micelle concentration (cmc) up to volume fractions of 0.18. Large osmotic pressures, up to 323 and 250 kPa for SDS and CPC, respectively, are interpreted as evidence of strong intermicellar interactions. To quantify these large osmotic pressures, we develop a self-consistent activity-coefficient model that includes explicitly the surfactant monomer, micellar aggregates, and electrolyte molecules. Excluded-volume effects are taken into account using the Boublik-Mansoori equation of state, and intermicellar electrostatic interactions are modeled using the mean spherical approximation (MSA). We combine the activity-coefficient model with an ideal mass-action model developed previously for the micelle equilibrium constants at infinitely dilute aggregate concentrations in the vicinity of the cmc.(1) The resulting nonideal thermodynamic model is used to describe the equilibrium between the micellar aggregates and the surfactant monomer at elevated concentrations. The Donnan membrane effect, which leads to the redistribution of background electrolyte, is accounted for within the thermodynamic framework of the model. Successful comparison is made between the proposed self-consistent model and the new experimental osmotic pressure data.