Abstract This work discusses the geopolymerization of lunar dust simulant JSC LUNAR-1A and Martian dust simulant JSC MARS-1A. The geopolymerization of JSC LUNAR-1A occurs easily and produces a hard, rock-like, material. The geopolymerization of JSC MARS-1A requires milling to reduce the particle size. Tests were carried out to measure, for both JSC LUNAR-1A and JSC MARS-1A geopolymers, the maximum compressive and flexural strengths. In the case of the lunar simulant, these are higher than those of conventional cements. In the case of the Martian simulant, they are close to those of common building bricks.