Using molecular dynamics (MD) simulation, we investigate the wave vector (k)-dependent dielectric relaxation in room-temperature methanol-water mixtures at three methanol mole fractions : x(m) = 0.2, 0.5, and 0.8. The simulations were carried out on systems of 500 molecules using the TIP4P and Hl effective pair potentials for water and methanol, respectively. We have calculated time correlation functions (TCFs) of the permanent dipole densities at k = 0 and of their transverse and longitudinal components at the five smallest-magnitude k values attainable in the simulations. Frequency-domain results in the form of the dielectric permittivity tensor, epsilon(k,omega), and the far-infrared (FIR) absorption coefficient are also reported. In order to assess the effects of intermolecular correlations on dielectric relaxation, we analyze the dipole density TCFs in terms of contributions from intraspecies autocorrelations, interspecies cross-correlations, and, in the k = 0 case, single-molecule dipolar autocorrelations. We find that interspecies cross-correlations strongly affect the intensity and relaxation rate of the collective dipolar TCFs and that short-ranged structural inhomogeneities play an important role in these properties, especially in methanol-rich mixtures. The transverse and the k = 0 TCFs are dominated by diffusive, but nonexponential, decay, which becomes more rapid as the mole fraction of water increases, while the longitudinal dipole density TCFs relax mainly through inertial and librational mechanisms. As the water concentration increases, the low-frequency librational bands in the FIR absorption coefficient diminish, while the hydrogen-bond librational band grows in width and intensity. We find that the transverse and longitudinal components of epsilon(k,omega) for the smallest-magnitude k values are essentially identical for frequencies above those which characterize the rotational-diffusion regime.