Viscoelastic behavior of insoluble monolayers of stearic, palmitic, pentadecanoic, and myristic acids has been studied by the method of capillary waves. The damping coefficient at the surface pressure close to zero displayed chaotic fluctuations indicating the inhomogeneity of the film. In this region the wave motion is determined by local values of the surface rheological properties. The observed fluctuations changed abruptly at the end of the transition from macroscopic two-dimensional islands of denser phase to the more homogeneous film. This behavior is connected with the establishment of the connectivity of the islands in the heterogeneous monolayer and simultaneously indicates the complex structure of the monolayer. For compact monolayers the imaginary part of the complex dynamic surface elasticity have been estimated with the help of the dispersion equation for capillary waves. It has been shown that the wave motion in the gaseous/liquid-condensed (monolayers of stearic and palmitic acids) and liquid-expanded/liquid-condensed (monolayers of pentadecanoic and myristic acids) two-phase regions is determined by the real part of the complex surface elasticity.