Abstract The tensile deformation behavior of a range of supersaturated Mg–Al solid solutions and an as-cast magnesium alloy AM60 has been studied. The Mg–Al alloys were tested at room temperature while the alloy AM60 was tested in the temperature range 293–573 K. The differences in the deformation behavior of the alloys is discussed in terms of hardening and softening processes. In order to identify which processes were active, the stress dependence of the strain-hardening coefficient was assessed using Lukáč and Balı́k’s model of hardening and softening. The analysis indicates that hardening involves solid solution hardening and interaction with forest dislocations and non-dislocation obstacles such as second phase particles. Cross slip is not a significant recovery process in the temperature range 293–423 K. At temperatures between 473 and 523 K the analysis suggests that softening is controlled by cross slip and climb of dislocations. At temperatures above 523 K softening seems to be controlled by dynamic recrystallisation.