A process is disclosed for the in situ conversion and recovery of heavy crude oils and natural bitumens from subsurface formations using either a continuous operation with one or more vertical injection boreholes and one or more vertical production boreholes in which multiple, uncased, horizontal boreholes may extend from the vertical boreholes, or a cyclic operation whereby both injection and production occur in the same vertical boreholes in which multiple, uncased, horizontal boreholes may extend from the vertical boreholes. A mixture of reducing gases, oxidizing gases, and steam are fed to downhole combustion devices located in the injection boreholes. Combustion of the reducing gas-oxidizing gas mixture is carried out to produce superheated steam and hot reducing gases for injection into the formation to convert and upgrade the heavy crude or bitumen into lighter hydrocarbons. Communication between the injection and production boreholes in the continuous operation and fluid mobility within the formation in the cyclic operation is induced by fracturing, multiple horizontal boreholes extending from vertical boreholes, or other related methods. In the continuous mode, the injected steam and reducing gases drive upgraded hydrocarbons and virgin hydrocarbons to the production boreholes for recovery. In the cyclic operation, wellhead pressure is reduced after a period of injection causing injected fluids, upgraded hydrocarbons, and virgin hydrocarbons in the vicinity of the boreholes to be produced. Injection and production are then repeated for additional cycles. In both operations, the hydrocarbons produced are collected at the surface for further processing.