The formation of fourfold energy clusters in high J-multiplets of triatomic waterlike molecules is analyzed theoretically. The semiclassical method is used to determine the rovibrational energy surfaces and the effective adiabatic rotational Hamiltonians for the ground and excited bending states in these molecules. The adiabatic separation of the rotational and the internal molecular motion used in this paper enables significant insight into the mechanism of the strong rotation-vibration interaction in rapidly rotating molecules. The critical values of the angular momentum J(c), at which the bifurcation responsible for the clusterization effect occurs, are calculated. The results from the previous classical studies [see I. N. Kozin and I. M. Pavlichenkov, J. Chem. Phys. 104, 4105 (1996)] and quantum mechanical calculations [O. L. Polyansky, P. Jensen, and J. Tennyson, J. Chem. Phys. 101, 7651 (1994)] on the structure of the J-multiplects in the H2O molecule are revised and the formation of the fourfold energy clusters can now be considered well understood.