Numerical simulation results of the Black Sea circulation obtained by four ocean dynamics models are compared to each other and to in situ data in order to determine the features of the Black Sea deep-water circulation such as deep-water undercurrents. The year 2011 is chosen as the test period due to the availability of deep-sea observations, including ARGO profiles and ADCP current velocities. Validation of the simulation results is based on comparison with the temperature and salinity measured by the ARGO floats. Anticyclonic currents (undercurrents) under the cyclonic Rim Current are detected by the results of all numerical models near the North Caucasian coast. The main characteristics of undercurrents are consistent with in situ data on current velocity up to a depth of 1000 m obtained by the Aqualog probe at the IO RAS test site near Gelendzhik in June 2011. The analysis of the spatio-temporal variability of the modeled salinity and velocity fields reveals that the most probable origin of the undercurrents is the horizontal density gradient of seawater in the region.