Spectrum of one-particle excitations of the two-orbital degenerate Hubbard model by us was investigated. The metod, that was applied by us, follows elaborated to this model in ref [1], the procedure to calculate and to using of the Green's functions of strong correlated electronic systems. The Hund coupling constant (J), the intra-orbital and interorbital Coulomb interactions (U,U`=U+2J) are the key interaction parameters. The states of the electronic system of any node are independent of the states of other nodes if you do not take into account the jumping electron between lattice sites. In that case the problem is reduced to the local Hamiltonian of one node. For the temperatures T ≠ 0, using eigenvalues Ei (i=1..16) and their associated eigenfunctions obtained in the Ref. [1] for the local Hamiltonian, we have calculated the average number of electrons at one node. The chemical potential, by use this average , has been considered as a function of the average number of electrons at one site (see Fig.1). As can be seen from Fig. 1, the jumps of chemical potential are well manifested at the passage to the filling with electrons of the next energy level after filling of the previous level. The gap between the energy levels determines the value of each chemical potential jump. The energetical gaps are changing when is changing the Hund constant coupling. The eigenvalues Ei (i=1..16) as functions on chemical potential are shown on the Figure 2. This dependences appear because the chemical potential was included in the local Hamiltonian. As can be seen from Fig.2 , the linear dependency on chemical potential of the eigenvalues Ei is not the same. This causes that the energy gap between the eigenvalues vanish at the points of intersection of their graphs. For the discussed model we have considered singleparticle energy spectrum of elementary excitations, taking into account the hopping of electrons between lattice sites in the case of half filling ( (3 5 ) / 2 0 μ = U − J ).It is shown that the Coulomb interaction between electrons on the lattice sites gives rise to an energy gap in the doubly degenerate band of free electrons. If take into account the interband interaction of free electrons, then each of the two degenerate bands splits into two subzones, which partially overlap.