Transfer functions of delay systems are hard to approximate by rational functions. This phenomenon, which is interesting
from the point of view of approximation theory, is also a concern in problems where the frequency response of a device must be approximated by a model
involving rational elements; for instance in identification and matching. In this talk, we derive a lower bound for the sup-norm approximation to a pure delay exp(-sT) (T the delay, s the complex variable) by a rational function of given degree on a finite interval of the imaginary axis, under a norm constraint on the error at all other points of the imaginary axis.