A pair of elevator cars (10, 11) traveling in the same hoistway have their positions sensed (20-23, 29-32) to provide for each a position signal (35, 37) from which velocity signals (64, 65) are derived; lookup tables (66, 61) of safe stopping distance (B, S) for braking and safeties are formed as a function of all possible combinations of velocity (V(U), V(L)) of said cars. Comparison of safe stopping distances for contemporaneous velocities of said cars with actual distance between said cars provides signals (85, 98, 99) to drop the brakes (49, 50) of one or more of the cars, and provides signals (82) to engage the safeties (18, 18a, 19, 19a) of all cars if the cars become closer or if acceleration detectors (117, 118) determine a car to be in freefall.