  For any arbitrary values of $n$ and $l$ quantum numbers, we present a simple
exact analytical solution of the $D$-dimensional ($D\geq 2$) hyperradial Schr%
\"{o}dinger equation with the Kratzer and the modified Kratzer potentials
within the framework of the exact quantization rule (EQR) method. The exact
energy levels $(E_{nl})$ of all the bound-states are easily calculated from
this EQR method. The corresponding normalized hyperradial wave functions $%
(\psi_{nl}(r))$ are also calculated. The exact energy eigenvalues for these
Kratzer-type potentials are calculated numerically for the typical diatomic
molecules $LiH,$ $CH,$ $HCl,$ $CO,$ $NO,$ $O_{2},$ $N_{2}$ and $I_{2}$ for
various values of $n$ and $l$ quantum numbers. Numerical tests using the energy
calculations for the interdimensional degeneracy ($D=2-4$) for $I_{2}, $ $LiH,$
$HCl,$ $O_{2},$ $NO$ and $CO$ are also given. Our results obtained by EQR are
in exact agreement with those obtained by other methods.
