This article reports on a remarkable natural ageing response observed for the first time in this work in Mg-Zn-based alloys. In these alloys, hardness in the naturally aged condition, generally, almost equals that in the artificially aged condition. The time to maximal hardness in the naturally aged condition can be dramatically reduced from several months needed for a binary Mg-Zn alloy, to a practical duration of a few weeks when some additional alloying elements that act as accelerants are added. Examples of such elements presented here are Cu and Ti. Strengthening in the naturally aged condition of these alloys is achieved through the formation of a very high density of Guinier-Preston (GP) zone-type precipitates. Both Cu and Ti also enhance the artificial ageing response by increasing the number density of the strengthening precipitates. Unlike Cu, Ti is not detrimental to the corrosion resistance and the current results indicate that it also has a very pronounced grain-refining effect on the Mg-Zn-based alloys.