In order to compare plastic deformation along different loading axes, icosahedral Al-Pd-Mn single quasicrystals were deformed in uniaxial compression along twofold and fivefold axes, between the lowest temperatures where deformation at strain rates of 10-5 and 10-4 s-1was possible and 820 °C. For the first time, experiments were performed below 680 °C. The strain rate and temperature sensitivity of the flow stress were studied by stress relaxation and temperature change tests. In a range of strain of steady state deformation following a yield drop, the flow stress and its strain rate sensitivity increase strongly with decreasing temperature. The temperature sensitivity shows a maximum at about 700 °C. The data hardly depend on the specimen orientation. Repeated relaxation tests indicate changes in the microstructure during the relaxations. Transient phenomena also occurred when the relaxation tests had not been started from steady state deformation, e.g. before the upper yield point, after long relaxations or after unloading. The results will be discussed in Part II of this paper.