In this paper we give useful convergence criteria for Hermite-Fejer interpo-lation Hn(f, x) , One of them is: Hn(f,x) converges uniformly to f(x) if and only if the norms of Hn(f,x) are uniformly bounded for all n and Hn(xk , x) converges uniformly to xk for k=l,2. |