Oscillations superimposed on steady shear flows have been used repeatedly in the past to determine the relaxation modes in flowing associative polymers. In these experiments, the oscillatory motion has been parallel to the steady-state now. Here, parallel superposition moduli on associative polymers will be compared with superposition experiments in which the oscillatory motion is perpendicular to the steady-state flow. In the latter experiments, there is less interference between the steady flow and the superimposed oscillations, which has drastic consequences for the results. Data are shown for a HASE polymer (hydrophobic alkali-swellable emulsion). As in other fluids, the limiting viscosities at zero frequency differ drastically, and negative storage moduli can be obtained in parallel superposition. The apparent relaxation frequencies during flow, as derived from parallel superposition measurements, are an order of magnitude smaller than those derived from orthogonal superposition. The effect of shear rate on the average relaxation times seems to be qualitatively similar in the two superposition modes, but the moduli-frequency curves differ in shape. The shapes of these curves also reflect the associative nature of the polymers.