In a rope of a lifting device, particularly of a passenger transport elevator and/or freight transport elevator, the width of which rope is greater than the thickness in the transverse direction of the rope, which rope includes a load-bearing part in the longitudinal direction of the rope, which load-bearing part includes carbon-fiber reinforced, aramid-fiber reinforced and/or glass-fiber reinforced composite material in a polymer matrix, and which rope includes one or more optical fibers and/or fiber bundles in connection with the load-bearing part and the optical fiber and/or fiber bundle is laminated inside the load-bearing part and/or the optical fiber and/or fiber bundle is glued onto the surface of the load-bearing part and/or and that the optical fiber and/or fiber bundle is embedded or glued into the polymer envelope surrounding the load-bearing part, as well as to a condition monitoring method for the rope of a lifting device.