Molecular orientation in aqueous lyotropic solutions of hydroxypropylcellulose has been studied in steady and transient flows using the technique of flow birefringence. Birefringence is an increasing function of steady shear rate in the range from 0.01-100 s-1. Upon flow cessation, the orientation is seen to decrease towards a globally isotropic condition. It is hypothesized that this decrease in orientation may reflect a transition from a flow-induced nematic back to a cholesteric phase. In this case, low orientation and "region I" shear thinning at low rates may be consequences of persistence of cholestericity in slow flows. The decrease in orientation appears to be well correlated with gradual increases in the complex modulus of the solution during relaxation. However, while birefringence reveals that the final state is optically isotropic for all previous shear rates, the long-time value of the modulus depends strongly on previous shear rate. To further investigate structural differences in the relaxed state, shear stress and birefringence were measured upon flow resumption. If the relaxed state resulted from a high previous shear rate, a very large overshoot is observed in stress, while if the previous shear rate is low, a much weaker oscillatory pattern is observed. Birefringence results are quantitatively similar. Finally, birefringence and stress were studied upon flow reversal. Both exhibit damped oscillatory responses, but the qualitative shape of the profiles change as a function of shear rate within the linear regime. These results are compared and contrasted with the behavior of liquid-crystalline solutions of poly(benzyl glutamate).