Sharp bounds for the zeros of symmetric Kravchuk polynomials K (n) (x;M) are obtained. The results provide a precise quantitative meaning of the fact that Kravchuk polynomials converge uniformly to Hermite polynomials, as M tends to infinity. They show also how close the corresponding zeros of two polynomials from these sequences of classical orthogonal polynomials are.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)