We give a detailed QCD sum-rule analysis of the semileptonic decays D+→K̅ 0e+νe and D+→K̅ 0*e+νe. We use the standard method based on expansion in Euclidean distance as well as a new set of sum rules on the light cone. We compare the results with current experimental data and results from quark models. Special attention is paid to the t dependence of the form factors. We find from our sum-rule analysis that for the vector form factors the usual pole model approximation works perfectly well, but is not adequate for the axial-vector form factors.