The objective of this research is to study near-critical and super-critical combustion of droplets consisting of binary fuel mixtures. Experimental results are reported on the burning of fiber-supported droplets of mixtures of n-heptane and n-hexadecane, initially about 1 mm in diameter, under free-fall microgravity conditions. The ambient pressures range up to 3.0 MPa, extending above the critical pressure of both fuels, in room-temperature nitrogen-oxygen atmospheres having oxygen mole fractions of 0.12 and 0.13. Three-stage burning of the binary fuel droplets is observed, and the onset lime of the second stage is compared with the predictions of an existing theory. Experimental evidence of thermo-capillary and/or diffuso-capillary convection during the droplet burning is obtained. The results contribute to improving understanding of binary-fuel droplet-combustion processes at high pressures.