Compressive creep studies have been carried out on hot-pressed ZrB2-SiC (ZS) and ZrB2-SiC-Si3N4 (ZSS) composites in air under stress and temperature ranges of 93-140MPa and 1300 degrees C-1425 degrees C, respectively for time durations of approximate to 20-40h. The results of these studies have shown the creep resistance of ZS composite to be greater than that of ZSS. As the temperature is increased from 1300 degrees C to 1425 degrees C, the stress exponent of ZS decreases from 1.7 to 1.1, whereas that of ZSS drops from 1.6 to 0.6. The activation energies for these composites have been found as approximate to 95 +/- 32kJ/mol at temperatures 1350 degrees C, and as approximate to 470 +/- 20kJ/mol in the range of 1350 degrees C-1425 degrees C. Studies of the postcreep microstructures using scanning and transmission electron microscopy have shown the presence of glassy film with cracks at both ZrB2 grain boundaries and ZrB2-SiC interfaces. These results along with calculated values of activation volumes suggest grain-boundary sliding as the major damage mechanism, which is controlled by O2- diffusion through SiO2 at 1350 degrees C, and by viscoplastic flow of the glassy interfacial film at temperatures 1350 degrees C. Studies by transmission electron microscopy have shown formation of crystalline precipitates of Si2N2O near ZrB2-SiC interfaces in ZSS tested at 1400 degrees C, which along with stress exponent values <1 suggests that grain-boundary sliding involving solution-precipitation-type mechanism is operative at these temperatures.