Substitution off lie hydroxyl (OH) groups of cyclodextrins (CDs) by methoxy (OCH3) groups is likely to influence the microscopic properties of water inside the cavities of these molecules and in the surrounding hydration layers. We have performed atomistic molecular dynamics (MD) simulations of aqueous Solutions of beta-cyclodextrin (BCD) and its two methyl-substituted forms, dimethyl beta-cyclodextrin (DIMEB) and trimethyl beta-cyclodextrin (TRIMEB). The calculations reveal that the translational and rotational motions of water present either in the hydration layers or in the cavities of these macrocyclic molecules are slower than that of pure bulk water. Interestingly, it is noticed that the effect of confinement inside the cavity increases with substitution of the (OH) groups of file BCD molecule. Most importantly, it is revealed that the time scale of relaxation of the CD-water (CW) and water-water (WW) hydrogen bonds are correlated with the microscopic dynamics of water and their degree of confinement within file cavities of these molecules.