A new technique has been developed to determine the sum of the surface (excess) shear viscosity and surface dilatational viscosity for insoluble monolayers on a gas-liquid interface. The flow on the interface is produced by the rise and the subsequent spread of a laminar vortex pair which dilates the interface. The terms in the tangential component of the stress boundary condition equation for the interface are directly evaluated through measurements of the velocity in the liquid and on the interface, obtained through digital particle image velocimetry, and measurements of the unsteady surfactant concentration on the interface, made with the nonlinear optical technique of second-harmonic generation. For the experiments, the water surface was initially covered by a uniform monolayer of hemicyanine dye, 4-[4-(dimethylamino)styryI]-1-docosylpyridinium bromide, which was chosen for its strong nonlinear optical response. The sum of the surface viscosities for hemicyanine was found to be 1.2 (+/-0.5) sp at a concentration of 0.65 mg/m(2).