An interfacial stress rheometer has been constructed to study the rheology of Langmuir films subjected to time-dependent flows. A magnetized rod resides at the air-water interface and is set into oscillation by applying a sinusoidal magnetic field gradient. Analysis of the amplitude and phase of the resulting rod motion relative to the applied force allows the determination of the dynamic surface modulus, G(s)*(omega), and measurement of the relative elastic and viscous contributions of the monolayer. Measurements at 22 degrees C were conducted on eicosanol (C-20) and mixtures of a rigid-rod polymer, phthalocyaninatopolysiloxane (PcPS), dispersed in eicosanol. The surface pressure dependence of the rheology for eicosanol reveals the presence of a maximum in the loss modulus, G(s)"(w), within the L-2＇ phase at Pi = 6 mN/m. In the LSI phase at pressures above 15 mN/m, the monolayer is Newtonian and has a surface viscosity of 0.03 mN.s/m. The mixtures of PcPS with eicosanol are known to have two-dimensional nematic behavior. The presence of PcPS in the film increased \\G(s)*(omega)\\ 100-fold, creating a non-Newtonian interface with a measurable elasticity. As the polymer rod concentration was increased further, G(s)*(omega) became less dependent on frequency, and above the isotropic-nematic transition, the storage modulus, G(s)＇(omega), exceeded the loss modulus, G(s)"(omega). The results on eicosanol and the mixtures of the rigid rod with eicosanol demonstrate that the rheometer is capable of detecting microstructural transitions in a Langmuir monolayer.