Surface dilatational dynamic elasticity ε of films formed by cross-linked poly(N-isopropylacrylamide) microparticles on a water/air interface has been determined as a function of polymer surface concentration Γ. The experimental dependences exhibit two maxima of ε at surface pressures π of nearly 6 and 35 mN/m. In the region of the second maximum, the pattern of the dependence is governed by a method used to vary Γ. At π > 25 mN/m, film compression leads to the formation of a metastable monolayer, while the gradual addition of a microparticle dispersion results in the establishment of equilibrium between the monolayer and surface aggregates. In the region of π values corresponding to the second maximum of ε, slow relaxation processes with a characteristic time substantially longer than 10 s occur in the system. At π > 35 mN/m, the film collapses due to the displacement of microgel particles from the water surface.