The fullerenes C60 and C70 were first identified in carbon vapour produced by laser irradiation of graphite, and have recently been produced in macroscopic quantities by vaporization of graphite with resistive heating. It has also been suggested that fullerenes might be formed in sooting flames, and indeed all-carbon ions with mass/charge ratios suggestive of fullerenes have been detected in flames. These species were assumed to have the cage structures of fullerenes, but the mass spectroscopic evidence could not establish this conclusively. We have now collected samples of condensible compounds and soot from hydrocarbon combustion under a range of conditions, and analysed these using conventional techniques in an effort to detect fullerenes. Spectroscopic studies reveal the presence of C60 and C70 in yields and ratios that depend on temperature, pressure, carbon/oxygen ratio and residence time in the flame. Control of these conditions allows optimal yields of 3 g of fullerenes per kilogram of fuel carbon burned, and variation of the C70/C60 ratio over the range 0.26-5.7.