Abstract: Let X be a r.v. in R^m. Consider the continuous type multi-parameter exponential families written in the form f(x, \theta) d \mu=C(\theta) \exp \left(\sum_i=1^s \theta_i t_i(x)\right) d \mu, where \theta=\left(\theta_1, \cdots, \theta_s\right) \in \Theta, T(X)=\left(t_1(X), \cdots, t_s(X)\right) is a sufficient statistic and we denote its marginal density by f(t) d \mu^T. Let the loss function be L(\theta, d)=\|\theta-d\|^2=\sum_i=1^s\left(\theta_i-d_i\right)^2. The prior distribution of \theta belongs to the family \mathscrF=\left\G: \int_\theta\|\theta\|^2 d G< \infty\right\. In this paper we have constructed the empirical Bayes (EB) estimator of \theta, \phi_n(t), by using the kernel estimation of f(t) and its first order partial derivatives. Under a quite general assumption imposed upon f(t), it is shown that \phi_n(t) is an asymptotically optimal EB estimate of \theta.