The quantum defects are studied for the doubly excited states of two-electron atom with one electron excited much more than the other. The dipole approximation for the electron-electron interaction allows the Rydberg series of the doubly excited states to be constructed with account for the electronic correlations. The latter are particularly important due to the high degeneracy of the atomic states when the electron-electron interaction is switched off. Most attention is paid to the semiclassical region of high total orbital momentum of the atom where closed analytical expressions are obtained for the quantum defect in the dipole approximation as well as for the Coulomb and exchange correction accounting for the residual electron-electron interaction in the first order of perturbation theory. The quantum defects for the Rydberg series of the helium atom and helium-like ions are calculated in the framework of asymptotic theory and compared with the data from energy level numerical calculations for the D and F series of He, Li⁺, Be²⁺, B³⁺.