A research of the occurrence factors of narrow non-stationary movements formed in the Black Sea in the lower part of the constant piccoline and deeper is performed. Such currents spread along the continental slope against the predominant cyclonic direction of surface circulation (undercurrents) are observed from several days to several weeks and have a width of 8 to 12 km. The prerequisites for the generation of undercurrents in the Black Sea hydrophysical fields are studied on the example of its north-eastern region, where the undercurrents are fixed most often. The numerical experiment results are analyzed to calculate the hydrophysical fields based on the numerical z-model of MHI with a horizontal resolution of 1.6 km. The experiment is carried out for the 2016-2017 period with assimilation in the model of hydrological observations of temperature and salinity. ERA5 data are used to set atmospheric forcing. The undercurrents are fixed twice in September 2016 and February 2017 according to the observations of the ARGO float ID6901833 in the area of the North Caucasus coast. A change in the direction of currents in the specified area (from cyclonic to anticyclonic and back) is reconstructed in the numerical experiment. Fields of basic hydrophysical parameters and some of their derivative characteristics are built and analyzed. The influence of mesoscale anticyclonic eddies, as well as gradients of the sea water density on the structure and variability of the velocity field in the north-eastern part of the sea is shown. According to the simulation results, narrow undercurrents into which Argo float fell in the fall of 2016 and in the winter of 2017 are distributed within a few days in the anticyclonic direction along the continental slope on horizons from 50–100 to 500 m, and their formation occurred under the conditions of weakening cyclonic Main Black Sea current in the upper layer of the sea and the increase in the Kerch anticyclonic eddy.