**MSC:**- 65L05 Initial value problems

gives a measure for the sensitivity of a solution w.r.t. small perturbations.

If we consider, however, {\em classes} of DAEs (e.g. all DAEs that arise

as semi-discretizations of a given partial DAE by the method of lines)

then the error bound in the definition of the perturbation index may become

arbitrarily large even if the perturbation index does not exceed 1.

We illustrate this fact by 2 examples and define as alternative the {\em uniform} perturbation index

that gives simultaneously error bounds for {\em all} DAEs of a given

class. We prove that in one example each individual DAE has perturbation

index 1 but the uniform perturbation index is 2. Another example illustrates

that the class of all finite difference semi-discretizations may even

have {\em no} uniform perturbation index if the given partial DAE has

perturbation index 2.