Brewster angle microscopy is used for investigations of nonequilibrium structures in 1-monopalmitoyl-rac-glycerol monolayers. The extent of branching of the condensed phase domains correlates with the supersaturation and thus with the compression rate of the monolayer. Dendritic growth is favored at intermediate compression rates, while tip splitting occurs at higher compression rates. The shape relaxation of unstable branched structures into nearly round equilibrium domains is shown by Brewster angle microscopy and described by a time development of the roundness. The optical anisotropy observed within the nonequilibrium structures allows the identification of the main growth direction of the dendrites with respect to the lattice directions.