The present invention relates to a rope and belt for a speed governor for elevators and associated sheaves that is applicable to speed governors for elevators. The rope comprises high-strength steel wires clustered in strands among which a core is in turn formed which is completely coated by a polymeric material which is introduced in the gaps defined between the strands, obtaining an outer polymeric surface with a diameter that is slightly greater than the diameter of the core. The belts cluster at least two metallic ropes comprising high-strength steel wires completely coated with a polymeric material. The sheaves designed for the ropes are semicircular or notched semicircular sheaves having a low aggression and reduced diameter and high level of adherence, determining a high coefficient of friction between the coated rope and the sheave, and a high strength of the rope against fatigue due to bending and wear is also obtained.