A theoretical study of the pulsed neutron problem and of steady-state neutron spectra has been made in mixtures of H2O and D2O in the temperature range 253 to 4°K. Mixtures with D2O content of 0, 5, 10, 15, and 20 wt% have been considered. For the pulsed neutron problem the multigroup Boltzmann equation in the diffusion approximation has been diagonalized to obtain asymptotic and transient spectra in assemblies with buckling values ranging from 0 to 0.6 cm-2 at 253, 77, and 21°K. The calculated values of the fundamental mode decay constant in various assemblies of ice at 253°K containing 20% D2O are found to agree very well with the experimental values reported by Salaita.For the steady-state problem, the multigroup inhomogeneous Boltzmann equation in the diffusion approximation has been solved by the matrix inversion method for different mixtures at 253, 77, 21, and 4°K. We show that there is an enhancement of cold neutron flux as the D2O content in ice is gradually increased. As in the case of H2O ice, we find that the mean energy of the neutron distribution goes on decreasing with decrease in ice temperature only as long as the temperature is above about 20°K. No further reduction in the mean energy of the neutron distribution is obtained when the temperature of the mixture is reduced below 21°K. It is shown that at 21°K, ice containing about 10 to 20% D2O is a better cold neutron source than pure H2O ice.