We report observations of phenomena within two-component Langmuir monolayers that are analogous to surfactant self-assembly in 3D solutions. A partially fluorinated fatty phosphonic acid played the role of 2D surfactant (linactant), and a perfluorinated fatty acid acted as the 2D solvent. Langmuir-Blodgett monolayers were prepared from mixtures of these compounds and examined using atomic force microscopy. Above a critical linactant mole fraction of similar to 0.013, distinctive monodisperse structural features were observed with a characteristic diameter of similar to 30 nm and a relative height of 1.4 nm. As the linactant concentration was further increased, the number density of these features increased linearly with concentration, whereas the size remained approximately the same. A quantitative analysis of these observations suggested that the features corresponded to self-limiting clusters composed of 2000 linactant molecules and that the dispersed clusters represented a 2D micellar phase. Above a linactant mole fraction of 0.63, the clusters organized into a local hexagonal structure with short-range positional order indicative of a 2D "lyotropic" liquid crystalline phase; the correlation length increased systematically with increasing linactant concentration.