An apparatus for opening and closing a car door and a shaft door of an elevator installation includes an entraining system (E) arranged at the car door and a cooperating locking mechanism (L). The entraining system (E) has a pair of spreadable entraining cams (1, 2) connected to first and second levers (3.1, 3.2) forming a parallelogram. A stationary guide rail (4.1) on the car has an entry cam (4) which receives a roller (5) on the entraining cam (1) to spread the parallelogram against a tension spring (6) and into engagement with first and second shaft lock rollers (7a, 7b) on the floor door to couple the doors together. The locking mechanism (L) has a transmission lever (8) attached to one entraining cam (2) and pivotally connected to a locking rocker (9) carrying a support roller (10). The locking rocker (9) also is pivotally connected with a catch (11) having a lug (11.2) that detents with a stationary lock plate (13) on the car to prevent opening of the car door. As the car door opens, the support roller (10) engages the support rail (12) on the floor door to pivot the catch (11) and release the lug (11.2) from the stationary lock plate (13) to unlock the car door.