There is an experimental evidence now that there is energy dissipation in the Non-Contact AFM (NC-AFM) system: energy is transfered to the surface. It has been recognised that this is a non-equilibrium process which has to be treated using methods of non-equilibrium statistical mechanics. There are two main mechanisms possible which can be responsible for the dissipation in the NC-AFM: (1) ``friction'' mechanism similar to that experienced by a Brownian particle in a solution and (2) so-called adhesion hysteresis mechanism which is due to strong interaction between atoms of the nano-tip and the surface. We have studied in detail the first mechanism using two methods: (i) coarse-grained distribution function and (ii) Non-Equilibrium Statistical Operator Method or NESOM (together with M. Y. Mo) and derived an expression for the friction force acting on the tip. This force is due to atomic vibrations of atoms at the surface and those of the nano-tip which are driven away from statistical equilibrium by constantly moving tip. The friction coefficient appears to be determined by the correlation function of the fluctuating part of the force. A work is being done on attempting the second mechanism using the NESOM.