The present work is focused on the investigation of the influence of a small volume fraction of nanoinclusions on the Miesowicz viscosity coefficient eta(2) of the nematic phase. Two kinds of nanoinclusions in the nematic phase have been studied: natural (smectic cybotactic clusters) and solid impurities (AEROSIL (R) 380). The volume fraction of nanoinclusions was estimated using the Batchelor model. This allowed in turn for calculating their number density. For cybotactic clusters, we found that their number in the nematic phase of octyloxycyanbiphenyl (8OCB) goes over the maximum when approaching the nematic-smectic phase transition. To shed some light on that finding we also studied eta(2) for a number of different AEROSIL (R) 380 suspensions in the nematic host of 4-trans-4'-n-hexylcyclohexyl isothiocyanatobenzene (6CHBT).