Curing technology of composite materials directly in space environment can be used for creation of large space structures in Earth orbit, on Moon, on Mars and other celestial bodies in future. The curing will be occurred under free space conditions such as high vacuum, temperature variations, cosmic radiation, microgravity and others. The space factors can significantly influence on the curing process and final properties of the composite. A space experiment on curing of the composite is complicate. At first stage, a laboratory experiment, computer modelling and stratospheric flight experiments are used for investigation of curing process. The results show a possibility of the curing and first prepreg of the composite was cured in stratosphere.