  We introduce a modified affine Hecke algebra $\h{H}^{+}_{q\eta}({l})$
($\h{H}_{q\eta}({l})$) which depends on two deformation parameters $q$ and
$\eta$. When the parameter $\eta$ is equal to zero the algebra
$\h{H}_{q\eta=0}(l)$ coincides with the usual affine Hecke algebra
$\h{H}_{q}(l)$ of type $A_{l-1}$, if the parameter q goes to 1 the algebra
$\h{H}^{+}_{q=1\eta}(l)$ is isomorphic to the degenerate affine Hecke algebra
$\Lm_{\eta}(l)$ introduced by Drinfeld. We construct a functor from a category
of representations of $H_{q\eta}^{+}(l)$ into a category of representations of
Drinfeldian $D_{q\eta}(sl(n+1))$ which has been introduced by the first author.
