Using addition theorems for Slater-type orbitals, obtained by the author with the help of complete orthonormal sets of Psi(alpha)-Exponential type orbitals (alpha = 1, 0, - 1, -2,...), the one-range addition theorems for arbitrary Yukawa-like central and noncentral interaction potentials and their first and second derivatives are established. The addition theorems derived for the interaction potentials and the Slater orbitals are especially useful for machine computations of arbitrary multielectron multicenter integrals that arise in the Hartree-Fock-Roothaan approximation, and also in the Hylleraas-correlated wave-function method, which play a significant role in the theory and applications to quantum mechanics of atoms. molecules. and solids. The obtained relationships are valid for arbitrary nonzero screening constants of the potentials.