Using expansion formulas for the translation of Slater-type orbitals (STOs) obtained with the help of complete orthonormal sets of Psi(alpha)-exponential type orbitals the addition theorems for STOs and interaction potentials are established. These addition theorems enable us to evaluate the multicenter t-electron integrals which arise in the solution of N-electron atomic and molecular problem (2less than or equal totless than or equal toN) when a Hylleraas approximation is employed in Hartree-Fock-Roothaan theory. The relationships obtained are valid for the arbitrary location, quantum numbers, and screening constants of STOs. (C) 2003 American Institute of Physics.