The mechanism of the adsorption in nanometric cylindrical pores has been studied using grand canonical Monte Carlo simulations. The results have been analyzed from the point of view of microscopic correlations. It has been shown that the correlations between the energy components and between the energy and the number of adsorbed particles provide crucial information concerning the microscopic mechanism of the formation of adsorbed layers. Typical susceptibility functions have been calculated. They give the relations between the statistical correlations and the stability of the adsorbed system in different stages of adsorption. The numerical calculations have been carried out for Kr atoms adsorbed in an MCM-41 model porous material with pores of diameter d = 4 nm. The smooth-wall model as well as the model of a wall with micropores have been discussed.