  We present a preliminary examination of a new approach to a long-standing
problem in non-Newtonian fluid mechanics. First, we summarize how a general
implicit functional relation between stress and rate of strain of a continuum
with memory is reduced to the well-known linear differential constitutive
relations that account for "relaxation" and "retardation." Then, we show that
relaxation and retardation are asymptotically equivalent for small Deborah
numbers, whence causal pure relaxation models necessarily correspond to
ill-posed pure retardation models. We suggest that this dichotomy could be a
possible way to reconcile the discrepancy between the theory of and certain
experiments on viscoelastic liquids that are conjectured to exhibit only stress
retardation.
