Recent developments in the synthesis of MAX phases have successfully introduced phases incorporating zirconium. These materials have been nominated for applications that experience high temperatures and irradiation damage. In this work, two newly synthesised zirconium-based MAX phases were investigated for their irradiation tolerance using high energy heavy ions at a variety of temperatures. The response of these materials to irradiation has been studied using scanning electron microscopy, transmission electron microscopy and X-ray diffraction. Zr2AlC MAX phase-based ceramic material with 33 wt.% ZrC has been irradiated with 22 MeV Au7+ ions between room temperature and 600oC, achieving a maximum nominal midrange dose of 3.5 displacements per atom. Under room temperature irradiation, the ions caused a partial amorphisation of the MAX phase. At high temperatures, irradiated Zr2AlC remained crystalline, but developed an increased density of dislocations and stacking faults in the (0001) basal planes. The irradiated material also exhibited a temperature-dependent microcracking phenomenon similar to that previously reported in other MAX phase materials. Zr3(Al0.9Si0.1)C2 MAX phase-based ceramic with 22% wt. ZrC and 10% wt. Zr5Si3 has been irradiated with 52 MeV I9+ ions at room temperature, achieving a maximum nominal midrange dose of 8.5 displacements per atom. Post-irradiation examination of the material revealed a number of crystalline changes to the MAX phase. At low doses, Zr3(Al0.9Si0.1)C2 maintained a high degree of crystallinity, while at the highest doses, the degree of crystallinity was greatly reduced. A number of radiation-induced phase transformations were observed, including the decomposition of Zr3(Al0.9Si0.1)C2 into ZrC and other phases, and the formation of 𝛽-Zr3(Al,Si)C2, a phase with a rearranged stacking sequence. Microstructural examination revealed that the majority of the extended defects in Zr3(Al0.9Si0.1)C2 lie in the basal planes. There was a poor damage recovery upon annealing the irradiated material to 300°C and 600°C.