Tensile tests are carried out for the aluminum alloys AA1200 and AA3103 at various strain-rates in the range from to . Tests with constant nominal strain-rate and strain-rate jump tests are conducted, and the instantaneous rate sensitivity and the rate sensitivity of strain hardening are investigated. For both materials, the instantaneous rate sensitivity is found to be rather independent of strain, while the rate sensitivity of the strain hardening is important and the saturation stress increases with increasing strain-rate. A phenomenological constitutive model is described that comprises a kinetic equation governing the instantaneous rate sensitivity of the flow stress and a structural parameter that determines the mechanical state of the material. The evolution of the structure parameter is assumed to depend on strain-rate. The model parameters are determined for the two materials using the available experimental information. It is found that the constitutive model provides a good representation of the experimental results.