  In this paper we generalize certain results concerning quantum affine algebra
$U_{q}(\hat{sl_{2}})$ at the critical level to the corresponding elliptic case
$E_{q,p}(\hat{sl_2})$. Using the Wakimoto realization of the algebra
$E_{q,p}(\hat{sl_2})$, we construct the central elements of it at the critical
level. It turns out that the so called Drinfeld conjecture originally proposed
for Kac-Moody algebras also holds for the elliptic quantum algebras.
