An in situ combustion process entailing the simultaneous production of liquids and combustion gases that combines fluid drive, gravity phase segregation and gravity drainage to produce hydrocarbons from a subterranean oil-bearing formation, comprising initially injecting a gas through a horizontal well placed high in the formation and producing combustion gas and oil through parallel and laterally offset horizontal wells that are placed low in the formation. wherein the reservoir exploitation proceeds with sequential conversion of production wells to injection wells in a line-drive mode of operation. The process may also be employed without in situ combustion, using instead a gaseous solvent or steam injection.