The phase behavior and the structural features of 1-stearylamine-rac-glycerol monolayers at the air-water interface are experimentally studied by surface pressure-area pi-A) isotherms, Brewster angle microscopy, and synchrotron X-ray diffraction at grazing incidence. The two-phase coexistence region defined for pi > 0 mN/m exists at temperatures of greater than or equal to 30degreesC. In comparison to the monoglycerol ethers, esters, and amides of the same alkyl chain length, the monoglycerol amines have the highest phase transition pressure. At equilibrium, circular, faceted, or cardioid domains subdivided in six or seven segments are formed in the two-phase coexistence region. Fractal-like nonequilibrium domain patterns g-row at usual monolayer compression. After compression stop, they are slowly transformed in the compact domains at equilibrium. The racemic 1-stearylamine-rac-glycerol monolayers have a rectangular-centered lattice structure. The tilt direction of the alkyl chains changes from NN to NNN already at low surface pressures. The low molecular ordering in the fractal-like condensed-phase domains is inferred from the fractal-like shape of the domains, the small position correlation length of < 50 mum, the high tilt angles at low surface pressure, and the beginning of pressure increase at comparably large areas per molecule.