An elevator arrangement, comprising at least one rope connected with an elevator car; a rope wheel arrangement (3a, 3b, 3c, 3d, 3e) comprising at least one rope wheel (3a1, 3a2; 3b1, 3b2, 3b3; 3c1; 3d1; 3e1, 3e2) around which the rope passes turning around an axis (x), which extends in width direction (w) of the rope; a rope position detector (4,5) arranged to detect displacement of the rope over at least one limit position and to trigger one or more predetermined actions in response to detecting displacement of the rope over a limit position, wherein the rope is arranged to pass around a rope wheel (3a1, 3a2; 3b1, 3b2, 3b3; 3c1; 3d1; 3e1, 3e2) turning around an axis (x), which extends in width direction (w) of the rope, and the rope position detector (4,5) is arranged to detect displacement of the rope over a limit position in thickness direction (t) of the rope at a detection point (p), and to trigger one or more predetermined actions in response to detecting displacement of the rope in its thickness direction (t) over the limit position, said limit position being on the opposite side of the rope than said rope wheel (3a1, 3a2; 3b1, 3b2, 3b3; 3c1; 3d1; 3e1, 3e2), characterized in that the departing point where the rope departs from the rim of the rope wheel (3a1, 3a2; 3b1, 3b2, 3b3; 3c1; 3d1; 3e1, 3e2) and the detection point (p) are at a distance from each other, where the distance is between 0.15 and 0.35 meters, wherein the rope is arranged to pass tangentially away from the rope wheel (3a1, 3a2; 3b1, 3b2, 3b3; 3c1; 3d1; 3e1, 3e2) further to the detection point (p) where it bypasses the limit position, and wherein the rope is a rod having a straight form when in rest state and elastically bendable away from the straight form. at least one rope connected with an elevator car; a rope wheel arrangement (3a, 3b, 3c, 3d, 3e) comprising at least one rope wheel (3a1, 3a2; 3b1, 3b2, 3b3; 3c1; 3d1; 3e1, 3e2) around which the rope passes turning around an axis (x), which extends in width direction (w) of the rope; a rope position detector (4,5) arranged to detect displacement of the rope over at least one limit position and to trigger one or more predetermined actions in response to detecting displacement of the rope over a limit position, wherein the rope is arranged to pass around a rope wheel (3a1, 3a2; 3b1, 3b2, 3b3; 3c1; 3d1; 3e1, 3e2) turning around an axis (x), which extends in width direction (w) of the rope, and the rope position detector (4,5) is arranged to detect displacement of the rope over a limit position in thickness direction (t) of the rope at a detection point (p), and to trigger one or more predetermined actions in response to detecting displacement of the rope in its thickness direction (t) over the limit position, said limit position being on the opposite side of the rope than said rope wheel (3a1, 3a2; 3b1, 3b2, 3b3; 3c1; 3d1; 3e1, 3e2), characterized in that the departing point where the rope departs from the rim of the rope wheel (3a1, 3a2; 3b1, 3b2, 3b3; 3c1; 3d1; 3e1, 3e2) and the detection point (p) are at a distance from each other, where the distance is between 0.15 and 0.35 meters, wherein the rope is arranged to pass tangentially away from the rope wheel (3a1, 3a2; 3b1, 3b2, 3b3; 3c1; 3d1; 3e1, 3e2) further to the detection point (p) where it bypasses the limit position, and wherein the rope is a rod having a straight form when in rest state and elastically bendable away from the straight form.