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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 93–140 MPa and 1300°C–1425°C, respectively for time durations of ≈20–40 h. 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°C to 1425°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 ≈95 ± 32 kJ/mol at temperatures ≤1350°C, and as ≈470 ± 20 kJ/mol in the range of 1350°C–1425°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°C, and by viscoplastic flow of the glassy interfacial film at temperatures ≥1350°C. Studies by transmission electron microscopy have shown formation of crystalline precipitates of Si2N2O near ZrB2–SiC interfaces in ZSS tested at ≥1400°C, which along with stress exponent values <1 suggests that grain‐boundary sliding involving solution‐precipitation‐type mechanism is operative at these temperatures.