Effects of two-particle interactions in deformed nuclei are considered. The deformed nucleus is assumed to be replaced by a set of particles in a cylindrically symmetric harmonic oscillator potential, while the two-particle interaction is assumed to be of δ-function type. Fairly extensive calculations are performed in diagonalizing the interaction energies which exist between particles lying in degenerate levels in the above-mentioned potential. The characteristic energies and the explicit form of the eigenfunctions are tabulated. In particular it is noticed that the seniority number is a good quantum number for this sort of interaction. Several important features of the results are discussed, including the matrix elements of the E2 transitions.