In this work we report, for the first time, calculations of nuclear magnetic resonance parameters for the processes of multiproton-exchange and nonbonded-proton rotations in small, cyclic water clusters. The simultaneous proton exchange induces a large decrease in the oxygen shielding constants in both clusters, with a mean value of -52.6 ppm for the water turner and -50.1 ppm for the water tetramer. The (1(h)) J(OH) coupling constant between an oxygen nucleus and exchanging proton decreases (in absolute value) along the path, changes sign, finally reaching a value of 5-7 Hz. The changes in the NMR parameters induced by the nonbonded proton rotations are smaller. The calculated dependencies of the intermolecular spin-spin coupling constants upon rotation reveal that the largest changes are expected for the couplings transmitted through the hydrogen bond between the rotating and neighboring molecule which acts as a proton donor. The symmetry-adapted perturbation theory (SAPT) interaction energy calculations for each dimer forming the water trimer have allowed us to relate a strength of interactions within pairs of water molecules with coupling constant values. The predicted maximal values of the interaction-energy terms (energetically unfavorable orientations of the constituent dimers) along paths correlate with the extremal values of the spin-spin coupling constants, which mostly correspond to the maximal couplings along pathways.