It is known that there are both viscometric and quasi-viscometric flows such that the Rivlin-Ericksen tensors of order three and higher are zero. While all of the experimentally important viscometric flows are steady, there exist viscometric and quasi-viscometric velocity fields which are unsteady in the laboratory frame. Hence, it is of interest to discover whether an unsteady viscometric or quasi-viscometric flow is intrinsically unsteady. That is, is an unsteady flow in the laboratory frame of reference also unsteady in all frames of reference translating and rotating with respect to the first one, or is it indeed steady in another particular frame of reference? The solution of such a problem, originally posed by Zorawski to answer the intrinsic unsteadiness or otherwise of a given velocity held, is applied here to show that an unsteady viscometric flow and an unsteady quasi-viscometric flow, in each of which the Rivlin-Ericksen tensors of order three and higher are zero, are unsteady everywhere, except when the viscometric flow under consideration is equivalent to simple shearing, or a rigid body motion. (C)1999 Elsevier Science B.V. All rights reserved.