Derivation of macroscopic equations from the simplest dumbbell models is re
visited. It is demonstrated that the onset of the macroscopic description i
s sensitive to the flows. For Peterlin's approximation [Makromol. Chem. 338
, 44 (1961)] to Warner's finitely extensible nonlinear elastic spring-force
model [Ind. Eng. Chem. Fundam. 11, 379 (1972)] (FENE-P), small deviations
from the Gaussian solution undergo a slow relaxation before the macroscopic
description sets on. Some consequences of these observations are discussed
.