Fractional hydrocarbons are recovered from reclaimed plastic materials and/or from oily residues. The reclaimed plastic materials and/or residues are sorted according to type and compacted using a feed system (1,2,3,4) in the absence of air. Thereafter the compacted mass is fed to a melting tank (7) below the liquid level. There the compacted mass is heated, so that a separation occurs into a first liquid phase, a first gas phase and a residue fraction. Thereafter the liquid phase and the first gas phase are transported into an evaporation tank (20) in which a second liquid phase and a second gas phase are formed under continued heat input. The second liquid phase is transferred to a re-heater (23) and is additionally heated there under further heat input so that a third gas phase is formed. Thereafter the second gas phase from the evaporation tank (20) and the third gas phase from the re-heater (23) are conveyed to a cracking tower (27) where further cracking of the long-chained hydrocarbons into short-chained hydrocarbons takes place, and the resulting oil gas is then conveyed to a condenser (30) in which the oil gas is condensed to form liquid oil, wherein the oil constitutes the target product.