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The possibility of using epoxy prepregs (fabric impregnated with epoxy resin) for carcass-inflatable antennas on space nanosatellites was investigated. It is shown that the optimal method of obtaining such devices is the use of reactive mixtures of hot cure, when the chemical reaction of curing of antenna deployed in space occurs under the action of solar radiation. In this case, the antenna is put into orbit in the nanosatellite in a compact form and no additional mechanisms are needed to give it the final working shape. The rheological properties of the mixture of epoxy resin YD-128 with hardener TEAT-1, suitable for making hot-curing prepregs and its use in near-earth orbit, are investigated. The dependence of rheological properties on temperature, hardener concentration and curing time is established. With the help of computer simulation, the temperature is calculated, to which the antenna carcass can be heated in near-earth orbit under the influence of thermal radiation from the Sun and the Earth taking into account its orientation in relation to the sources of heat. It is established that the process of hot curing of the antenna is possible due to solar and terrestrial radiation only when the frame is covered with a thin metallized layer that is close in characteristics to the layer of aluminum foil.