Transient stresses in shear-rate-controlled experiments were measured for two nematic side-chain liquid crystal polymers (side-chain LCPs), a flow-aligning one and a non-flow-aligning one, over a range of different temperatures. The chemical structures of the LCPs differ in the number of methylene groups in the spacer linking the mesogenic side groups to the polysiloxane backbone. The LCP with the shorter spacer forms only a nematic liquid crystalline phase and is flow-aligning over the whole temperature range of this phase. In contrast, the LCP with the longer spacer has an additional low-temperature smectic phase and is a non-flow-aligning nematic. Damped time-dependent oscillations in both the first normal stress difference and the shear stress were found for the non-flow-aligning sidechain LCP, whereas a rheological response characteristic of a flow-aligning system was found for the other one. A comparison of the oscillating transients of the non-flow-aligning LCP with Ericksen＇s transversely isotropic fluid model shows good agreement for the shear stress but not for the first normal stress difference. The intensity of the stress oscillations in the non-flow-aligning system increases spectacularly alter prior squeezing or stretching of the sample. Its rheological response after flow reversal is in agreement with the previously observed "log-rolling" orientation of the mesogens. In the range of shear rates studied, both polymers are slightly shear thinning and show positive steady-state values of the first normal stress difference, which increases almost linearly with increasing shear rate.