We have built an apparatus to study the viscoelastic response and measure the complex shear moduli of Langmuir monolayers as functions of the frequency and amplitude of the applied sinusoidal shear strain. A rotor is placed in contact with the monolayer and suspended by a torsion wire; a coil attached to the rotor carries a direct current. The voltage induced in this coil by a high-frequency external magnetic field is used to measure the angle of rotation with an accuracy of ∼0.005°. A low-frequency external magnetic field is used to drive the rotor into forced oscillations at the desired frequency (1 mHz–1 Hz), or the rotor may oscillate freely with the “natural” frequency variable over the range 0.01–3 Hz using a static external magnetic field. The apparatus has a large dynamic range for shear modulus measurement (∼5×10−3–103dyn/cm), achieved by using the free oscillation (ring-down) method for films with low shear moduli (∼5×10−3–1 dyn/cm), and the forced oscillation method for films with higher shear moduli (∼1–103dyn/cm). We have found that the complex shear modulusGof heneicosanoic acid Langmuir monolayers depends on the applied strain except at very low amplitudes. We also present sample data showing the frequency dependence ofG. ©1997 American Institute of Physics.