<p>In this paper, we establish two local error bounds for the generalized polynomial complementarity problem. The first error bound is obtained by using the natural residual function; and the second error bound is obtained by using a residual function definited by the standard violation measure of the polynomial equalities and inequalities. These two error bounds improve the corresponding results obtained recently in the literature for the generalized polynomial complementary problem. Furthermore, when the generalized polynomial complementarity problem is reduced to a quadratic complementarity problem, the error bounds obtained also improve the corresponding results given in the literature.</p>