A large (80--90 km in diameter) anticyclonic eddy centered at 43¿N, 37--38¿E has been the subject of complex investigation in the summer-autumn of 1999 based on measurements carried out during the Black Sea'99 expedition on board of R/V Akvanavt (CTD surveys, deployment of Argos-tracked drifters), analysis of satellite imagery, and using altimetric sea level anomaly maps from merged TOPEX/POSEIDON and ERS-2 satellite data. The eddy was formed as a nearshore anticyclonic eddy (NAE) in the Sochi-Sukhumi region, separated from the coast on 6--9 April 1999, stayed at the center of the eastern basin, which is usually characterized by cyclonic circulation, during about 8 months and decayed near the Turkish coast in December 1999. A compilation of hydrodynamic situations of different years (1993, 1997--1999) suggests that similar open sea anticyclonic eddies are frequently the elements of the circulation in the eastern Black Sea in the warm season (April--December). A positive correlation appears to be between eddies' formation and weak macroscale circulation associated with low atmospheric wind forcing. Long lifetime of open sea anticyclones is likely determined by their interaction with neighboring eddies. NAEs' separation from the coast and their transformation into open sea eddies provide horizontal mixing of the upper layer waters and results in deflection of the Rim Current offshore, formation of large meanders of the current around the eddies, and its branching when rounding such features. An example of calculation of cross-shelf water transport relating to an offshore Rim Current branch is presented. It is pointed out that an estimation of the shelf/open sea water exchange based on the box balance model does not contradict the assumption that such exchange is considerably determined by NAEs' separation from the coast.