For analytic functions we give an expression for the kernel $K_n$ of the remainder terms for the Gauss-Radau and the Gauss-Lobatto rules with end points of multiplicity r and prove the convergence of the kernel we obtained. The error bound are obtained for the type $$mid$R_n(f)$mid$ leq frac{1}{pi}l(Gamma) max_{z in Gamma} $mid$K_n(z)$mid$ max_{z in Gamma} $mid$f(z)$mid$$</TEX>, where $l(Gamma)$ denotes the length of contour $Gamma$.