An apparatus for sterilizing cap-like container closures includes a transport system for moving closures through treatment zones. The first zone preheats the closures, the second exposes them to a sterilizing agent, and the third activates or dries them. The first and third zones each have a rotor that circulates about a rotor axis thereof, and closure holders formed on a periphery thereof for moving closures through the first zone from a closure pickup disposed therein to a first closure delivery position, and through the third zone from a second closure delivery position disposed therein to a closure discharge. The second treatment zone is between the first and second closure delivery positions such that closures delivered to the first position, after passing the second zone and after exposure to the sterilizing agent, are passed on to a closure holder ready at the second position of the rotor in the third zone.