The two-dimensional fluid dynamics of the different phases of a fatty acid monolayer (docosanoic acid) were examined. Brewster angle microscopy was used to investigate the polydomain structure of two "liquid condensed" phases (the L(2) and L’(2) phases) and the "solid" (S) phase in situ during an extensional flow. Only the L(2) phase deformed affinely with a liquid-like response, The two other phases experienced flow-induced reorientation of the lattice onto which the molecules were arranged, The reorientation process was accompanied by the appearance of shear bands in the monolayers at an angle of +/- 45 degrees to the extension axis of the flow.