Extensive experimental information is available about the theological behaviour of liquid crystalline polymers, especially the stationary-flow behaviour. Only recently models that describe some of the transient-flow properties of the materials under consideration also have been suggested. It turns out that the various features are always more pronounced in the normal stresses than in the shear stresses. Therefore, the time evolution of the normal stresses could be very useful for evaluating existing models and in guiding further modelling. Yet, no systematic data of this nature are available in the literature. Here, data are presented on the time-dependent response of shear stresses and first normal stress differences to stepwise changes in shear rate. Flow reversal, stepwise increase in shear rate and stepwise decrease in shear rate are considered for two lyotropic systems : a solution of polybenzylglutamate and one of hydroxypropylcellulose. Scaling laws for the stress transients are investigated. Depending on the type of transient how, two types of scaling behaviour are observed for both shear and normal stresses; they are compared with theoretical arguments. For each type of transient experiment, a characteristic interrelation between shear stress and normal stress is obtained which should prove very useful in model evaluation.