The Sturmian hydrogenoid orbitals form a basis set (complete with no need for inclusion of the continuum) which can be usefully exploited for the solution of atomic and molecular structure problems. They are connected in momentum space with hyperspherical harmonics and in configuration space with Slater-type orbitals. In this work we give exact formulas and computational recipes for nuclear attraction integrals involving both the polar and the parabolic (or Stark) Sturmian set. These integrals are needed for the matrix elements entering the secular problem for the construction of molecular orbitals within the Bom-Oppenheimer scheme. Such a secular problem can be formulated at different iteration levels for the one-electron Schrodinger equation, and their relative performances against truncation are quantitatively assessed. (C) 2002 Elsevier Science B.V. All rights reserved.