Abstract The paper presents an investigation on the effect of process variables and material condition on forgeability of magnesium wrought alloys of Mg–Al–Zn group, AZ31 and AZ61. The experimental work includes studies of forging capabilities of the alloys in closed-die forging at hot and warm-working temperatures. Forging tests were performed for material both in as-cast and as-worked condition, for two variants of workpiece geometry. The different variants of the workpiece indicated fracture-related problems in forging magnesium alloys in the warm-working temperature regime, which involved interaction between material condition and process variables, and state of stress. By means of numerical calculations it was concluded, that in addition to material condition, a favourable state of stress, provided by a closed-die, can greatly improve the forgeability of AZ Mg alloys in the warm-working range.