In this paper are presented the influences of the adhesion forces occurring in hyperbolic micro contact on the oil velocity and friction forces in hyperbolic micro bearing gap. Here are elaborated the dependences between adhesive forces and oil dynamic viscosity in super thin boundary layer and influences of adhesive forces on the oil velocities and friction forces in micro- and nano-scale arising between two cooperating hyperbolic surfaces in micro-bearings. Oil dynamic viscosity is a sum of classical viscosity and viscosity caused by adhesion and cohesion forces. In hyperbolic micro-bearing the influence of adhesive forces on friction forces is visible not only in friction forces caused by the hydrodynamic pressure but also in friction forces caused by the oil flow velocity. The pressure distributions and capacity values in machine hyperbolic slide micro-bearings are determined in the lubrication region which is defined on the micro-bearing surfaces. Numerical calculations are performed in Mathcad 14 Professional Program implemented by virtue of difference method. In this paper are derived the formulas for velocity components, pressure distributions, friction forces and friction coefficients in hyperbolic coordinates and at the same time the adhesion forces are considered. Up to now the influence of adhesion forces on oil velocity and friction force changes in hyperbolic micro-bearing gap were not considered in analytical way. Present paper elaborates the preliminary assumptions of hydrodynamic theory of lubrication for hyperbolic micro-bearing in the case if during the lubrication the adhesion forces are taken into account.