The twofold degenerate Anderson impurity model [1-4] is investigated in normal and superconducting states, and the strong electronic correlations of d-electrons of impurity ion are taken into account by elaborating a suitable diagram technique. We discuss the properties of the Slater-Kanamori model [2-4] of d-impurity electrons. After finding the eigenfunctions and eigenvalues of all 16 local states, we determine the local one-particle propagator. Then we construct the perturbation theory around the atomic limit of the impurity ion and obtain the Dyson type equations between impurity electron propagators and normal and anomalous correlation functions. By summing infinite series of ladder diagrams, the approximation for correlation functions is established. The criterion for appearance of a superconducting state of the model is discussed.