Creep is a time-dependent deformation of materials under stress at elevated temperatures. The phenomenon of creep allows materials to plastically deform gradually over time, even at stress levels below its yield point or below its transformation temperature. The issues involving creep are especially significant for magnesium alloys, since they are susceptible to creep deformation from temperatures as low as 100 ºC, which inhibits their potential application in areas such as automotive engines. The University of Canterbury has developed a significant level of experience and infrastructure in the field of Electron Backscatter Diffraction (EBSD). EBSD allows microstructures to be characterized by imaging the crystal structure and its crystallographic orientation at a given point on a specimen surface, whereby the process can be automated to construct a crystallographic “orientation map” of a specimen surface. In light of this, the creep of magnesium and its alloys was studied using a novel technique, in which a conventional tensile creep test was interrupted at periodic intervals, and the EBSD was used to acquire the crystallographic orientation maps repeatedly on a same surface location at each interruption stages. This technique allows simultaneous measurement of the rate of creep deformation and the evolution of the specimen microstructure at various stages of creep, bringing further insight into the deformation mechanisms involved. This thesis summarizes the study of the microstructural and crystallographic texture evolution during creep of pure magnesium and a creep resistant magnesium alloy Mg- 8.5Al-1Ca-0.3Sr. Pure magnesium exhibit a conventional “power-law” type creep, and although its creep properties are well established in the past literatures, there has been little in terms of reconciliation between the observed creep rates and the underlying deformation mechanisms. The alloy Mg-8.5Al-1Ca-0.3Sr, on the other hand, is a modern die casting alloy used in the automotive industry for engine and gearbox applications, and despite its superior creep resistance, little is known about the microstructural contributions to its creep properties. This research was conducted to provide a link between the creep properties, observed microstructures, and theories of creep deformation by the use of advanced microscopy techniques. For the first time, the detailed, sequential microstructural development of magnesium and its alloys during creep has been revealed.