Mixtures of water or D2O + 1,4-dioxane (DX) have been studied at 25 degrees C by dielectric relaxation spectroscopy over a wide range of frequencies (0.2 <= nu/GHz <= 89) for DX mole fractions 0 <= x(2) <= 0.67. The spectra were best fitted by the sum of two Debye terms. The slower process was assigned to the cooperative relaxation of the hydrogen-bond network of water, whereas the faster mode reflects the dynamics of H2O molecules in a DX-rich environment. Analysis of the relaxation parameters revealed a largely microheterogeneous structure of the mixtures. The marked slowing-down of the cooperative mode on addition of DX is ascribed to the reduction of available H-bond acceptor sites and geometrical constraints on the H2O molecules in the water-rich regions.