An apparatus (1) for sterilizing container closures comprises a conduit (2) defining a passage for the closure and having a wall (3) surrounding the passage, spraying means (4) for injecting inside the conduit (2) a sterilization fluid heated and vaporized, drying means for introducing hot air in the conduit (2) and means for capturing the exhaust fluids exiting from the con-duit (2), said means comprising at least a suction hood (15) arranged over a corresponding exhaust opening (14) defined in the conduit (2) at a predetermined distance thereto, to capture the exhaust fluids from said exhaust opening (14) bay way of a draught effect.