The available information on the two particle doublets in the deformed even-even rare-earth nuclei is examined to reveal that presently, on average, only one doublet per nucleus has been experimentally identified up to 3 MeV excitation energy for the nuclei in the region from 156Gd to 182W. Consideration of the superposition of the single particle Nilsson orbitals available from the neighbouring odd-mass nuclei suggests the occurrence of over twenty such doublets in each of the nuclei. We present a formalism for the prediction of the complete two-quasineutron and two-quasiproton band structures in these nuclei based on the residual interaction calculations. Detailed results for the nucleus 168Er are presented in comparison with the available experimental information to illustrate the application of this formulation. The characteristics of the residual interaction are compared for the odd-odd and the even-even regions.