Dielectric spectra from 200 MHz up to 3 THz were determined to study the fast dynamics of dilute water + 1,4-dioxane. epsilon(nu) could be fitted by a collision induced oscillator at high frequencies plus two Debye relaxations in the microwave region. Isotope substitution was used to assign water and dioxane modes. The presence of the cooperative hydrogen-bond network relaxation down to a water mole fraction of 0.005 suggests a microheterogeneous structure of the mixtures even at low water content. The collision mode of dioxane at similar to 2 THz grows upon water addition, revealing the presence of H2O molecules in dioxane-rich domains.