Method steps and apparatus combinations for continuous in-line polymeric coating of rigid corrosion-protected flat-rolled sheet metal continuous-strip substrate utilizing a thermoplastic polymeric material having adhesive characteristics, capable of molten thin-film extrusion for chemical-bonding with an activated-surface of the flat-rolled sheet metal substrate, and substantially-simultaneously bonding with a solid-film polymeric material, establishing a work-product embodiment with multiple-polymer-layers traveling with the single activated surface; and, on which the solid polymeric film is selected to provide strength, hardness and other desired surface mechanical properties which also provide for external surface coloration, design, weather-proofing, and fabricating capabilities. A second embodiment provides dual-surface multiple-polymeric layer coating carried on by activating and polymeric coating one surface, at a time, of rigid corrosion-protected flat-rolled sheet metal continuous strip substrate.