In this chapter, we consider joint L2-eigenfunctions on pseudo-Riemannian locally homogeneous spaces denoted by XΓ = Γ\G/H. In previous work, we constructed nonzero generalized Poincaré series by averaging Flensted-Jensen’s functions over Γ-orbits on X, and derived L2-eigenfunctions on XΓ under certain conditions. These conditions include the requirement that X be a symmetric space satisfying the Flensted-Jensen–Matsuki–Oshima rank condition, and that the action of Γ on X satisfy a strong properness condition called sharpness. However, there also exists discrete spectrum that cannot be obtained through this method. In this chapter, we introduce a definition of discrete spectrum (and joint eigenfunctions) categorized into type I and type II. The joint eigenfunctions obtained using the aforementioned generalized Poincaré series belong to type I. Joint eigenfunctions of type II are characterized by the property that they are orthogonal to those of type I.