Quantum four-dimensional model calculations of the coupled intermolecular torsional vibrations of the cyclic homodromic water tetramers (H2O)(4) and (D2O)(4) are presented, based on the analytical modEPEN4B potential energy surface [S. Graf and S. Leutwyler, J. Chem. Phys. 109, 5393 (1998), preceding paper] and a four-dimensional discrete variable representation approach. The lowest 50 torsional levels were calculated up to 420 and 500 cm(-1) for (D2O)(4) and (H2O)(4), respectively. For both clusters, the torsional ground state is split by a synchronous O-H torsional inversion process, similar to inversion tunneling in ammonia, with calculated tunnel splittings of 21.8 and 0.000 12 MHz for (H2O)(4) and (D2O)(4), respectively. As for the cyclic water trimer and pentamer, the four torsional fundamentals of the tetramer lie above the torsional interconversion barriers, between 185-200 cm(-1) for (D2O)(4) and 229-242 cm(-1) for (H2O)(4), but also lie below the one-dimensional torsionally adiabatic barriers. The anharmonic fundamental frequencies lie both above and below the normal-mode frequencies, by up to 33%. Slightly above the fundamental torsional excitations, at 257-260 and 280-281 cm(-1) for (H2O)(4) and (D2O)(4), respectively, lie four states corresponding to four versions of the {uudd} isomer, which form a pseudorotational manifold; the torsional interconversion occurs by a sequence of double O-H flips. Higher excited pseudorotational states are calculated up to a vibrational angular momentum of k = 3. At approximate to 295 and approximate to 300 cm(-1), a further group of eight states is found, corresponding to the eight permutationally equivalent versions of yet another isomer, the {uuud} structure. The four {uudd} and eight {uuud} states of (H2O)(4) exhibit inverse isotope effects, and lie at lower energy than their (D2O)(4) counterparts.