It is shown that the square-root van Hove singularity appearing in the density of states ?(EF)~(EF-E0)-1/2 as a result of extended saddle-point singularities in the electron spectrum of high-Tc superconductors based on hole-type cuprate metal-oxide compounds gives a nonmonotonic dependence of the critical temperature Tc on the position of the Fermi level EF relative to the bottom E0 of the saddle. Because the divergence of ?(EF) is canceled in the electron-electron interaction constant renormalized by strong-coupling effects, Tc approaches zero as EF?E0, in contrast to the weak-coupling approximation, where in this limit Tc approaches a finite (close to maximum) value. The dependence obtained for Tc as a function of the doped hole density in the strong-coupling approximation agrees qualitatively with the experimental data for overdoped cuprate metal oxides. © 1998 American Institute of Physics.