Classical trajectory calculations for the unimolecular dissociation of nonrotating H2O, DHO, and MuHO are reported for different distributions of energy among the three vibrational normal modes. The calculations employ a realistic energy-switching potential energy surface for the electronic ground state of the water molecule. It is found that the unimolecular decay rates vary with the vibrational mode of the water molecule that is initially excited. Mode-selectivity has also been observed for DHO and MuHO, with the results being rationalized from inspection of the eigenvectors of the corresponding excited normal mode.