Through thermodynamic arguments, it is shown that the rest state of a viscoelastic fluid with fading memory is stable to the class of retarded flow perturbations, for which the second‐order approximation to the stress isS=−pI+β0A1+β2A12+β1A2,even thoughβ10,β1+β2=0,β1⩾0.In the absence of the latter two conditions, asymptotic stability is not assured.