Using expansion formula for the translation of Slater-type orbitals (STOs) obtained with the help of Coulomb Sturmian exponential-type functions (ETFS) (Guseinov, I. I. Int J Quantum Chem 2001, 81, 126) the multicenter electron-repulsion integrals are expressed in terms of the basic overlap integrals with the same screening parameters and the two-center basic hybrid integrals. For the calculation of basic hybrid integrals the recurrence relations are derived. These recurrence relations enable us to calculate some basic hybrid integrals by the use of which other basic integrals are calculated analytically from the formulas in terms of new auxiliary functions introduced recently by the authors. The recurrence relations obtained in this work for basic hybrid integrals are especially useful for the calculation of multicenter electron-repulsion integrals for large quantum numbers of STOs. (C) 2002 John Wiley Sons, Inc.