The existence of a tongue of Mediterranean Water (MW) at the depths of 500–1500 m is a characteristic feature of the hydrological regime in the northeastern part of the Atlantic Ocean. Anticyclonic eddies filled with MW (meddies or lenses) are observed in this region. They are identified via their high temperature and salinity anomalies, which compensate in density, yielding nearly homogeneous meddy cores. The analysis of historical observations has showed that approximately 100 lenses can exist simultaneously in this part of the ocean. High concentration of large water volumes (>4000 km3 each) can be found both in the region of their origin near the Iberian Peninsula and near the Azores Frontal Zone. The latter is precisely the region in which merging of eddies can occur to form larger lenses. The existence of long-living lenses at large distances from the region of their formation is an indirect indication of the fact that merging of lenses occurs (MESOPOLYGON lens, SM1 lens in the SEMAPHORE experiment, and a lens in the Sargasso Sea). Here, we analyze the results of model experiments on interaction between two anticyclonic eddies applying the contour dynamics method (CDM) to a three-layer ocean. In these experiments, the vertical distribution of layerwise density in the layers, the horizontal size of the eddies (assumed to be cylindrical structures), and their depth location correspond to the observed conditions in the Atlantic Ocean. We show that the evolution of intrathermocline eddies and the evolution of barotropic eddies differ significantly. We found the behavior of interacting eddies in the middle layer depends on the Froude number. We determined the critical distances between the lenses when their merger begins and the destruction' criterion for the elliptical intrathermocline eddies.