Multicenter integrals with integer and noninteger values of indices u of Yukawa-type screened Coulomb-type potentials (SCTPs) f(u)(eta,r)=r(u-1)e(-etar) and their derivatives over Slater-type orbitals (STOs) are evaluated using series expansion formulas obtained from the expansions in terms of complete orthonormal sets of Psi(alpha)-exponential-type orbitals (Psi(alpha)-ETOs, alpha=1, 0, -1, -2,...). The final results obtained are valid for the arbitrary values of parameters of SCTPs and STOs. (C) 2004 American Institute of Physics.