A rheological study on a two-dimensional Langmuir monolayer has been conducted by measuring the optical anisotropy and the mechanical surface properties. Experiments were conducted on monolayer mixtures of a liquid crystalline polymer, poly(p-phenylene)sulfonic acid (PPPSH), with an aliphatic fatty acid, stearic acid (C-18). It is found that these two molecules mix ideally, as supported by studies of average molecular area, collapse pressure, and Brewster angle microscopy. Both surface moduli and surface viscosity were obtained with an interfacial stress rheometer and showed that PPPSH/stearic acid monolayer mixtures are non-Newtonian. The orientational dynamics of polymers under well-defined planar extensional flow was considered using UV dichroism, which revealed a surface pressure-induced isotropic-nematic transition. This transition is difficult to observe using traditional isotherm analysis; however, it is readily evident in measurements of the rheology of the monolayers.