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This paper studies the qualitative properties of the spline approximation scheme for retarded functional differential equations introduced by Kappel and Salamon [SIAM J. Control Optim., 25 (1987), pp. 1082-1117. It is shown that the approximating systems are stable for large N if the underlying retarded functional differential equation is stable. In this case the approximating equations are in some sense uniformly (with respect to the approximation index) stable in the vector component of thedoi:10.1137/0327021 fatcat:kgtn5zd5ufg47aoq73quhwuwei