Nuclear magnetic relaxation measurements were used to determine activation energy E-act of the motion of water molecules adsorbed in active carbons. The E-act value was found to depend on the filling of active carbon pores due to changes in the state of water molecules under adsorption. It was established that the E-act = f(p/p(s)) plots, where p/p(s) is the relative pressure of water vapor observed for microporous active carbons (FAS-1, 2, N-15, SKT-6A), are similar in form to the corresponding plots of changes in water adsorption heats. In particular, we concluded that the plateau in the E-act = f(p/p(s)) dependences, as in the case of adsorption heats, reflects the volumetric filling of active carbon micropores with water. We show that a linear function describes the increase in E-act values for water upon the complete filling of micropores with an increase in the volume of adsorbed water clusters per one primary adsorption center (W-0/a(m)). We establish that, for water in the FAS-3 sample, the deviation of E-act values from this linear function was due to the contribution from the vapor phase in the mesopores (x(0) = 0.7-1.2 nm) that make up a considerable part of the active carbon's porous system.