A seat-cover or the back-cover strip for motor-vehicles seats is formed by a band made of a thick but flexible open-work fabric, upper anchoring elements and lower anchoring elements. The strip can include one or more cushions having different shapes and thicknesses, with or without a lining, acting as lumbar and/or spinal supports, fixable on the seat under the band itself. The upper anchoring elements generally include one or more threads for fixing the strip to support bars of a headrest, and at least one rod, having a polygonal cross-section, which cooperates with the one or more threads. The lower anchoring elements include at least one pipe and at least one tape having at least one hook joinable to the free end of a further tape, partially folded on itself and forming a stop for a loop-shaped thread, fixable to the portion under the base of the seats.