The nonstationary process of filmwise condensation of vapor on curvilinear fins with condensate suction from interfin grooves is numerically simulated with account taken of surface tension and gravity. The problem is reduced to solving a nonlinear evolution equation for the thickness of the condensate film. We performed calculations of the ethanol vapor condensation at atmospheric pressure on the fins of constant curvature for various temperature differences between the fin surface and the vapor saturation and for various values of the rate of condensate suction from the interfin space. Numerical calculations show that the condensation process is stable in the device (i.e., in the condenser) with condensate suction. Filling the interfin space leads to diminishing the zone of intense condensation and reducing the condensate inflow; therefore, this yields stable equilibrium between the condensation and condensate suction. The changes of the condenser temperature at a constant condensate suction entail variation of the filling level of the interfin groove and establishment of a stationary process, provided that the fin temperature becomes constant.