Abstract: A thermally-tuned rotary labyrinth seal for a gas turbine engine includes an inner annular seal member having axially spaced, radially projecting annular seal teeth, and an outer annular seal member having a stepped honeycomb structure which face the annular seal teeth of the inner seal member and define therewith axially spaced regions bounded by the seal teeth and honeycomb structure. The seal teeth and stepped honeycomb structure cooperate to inhibit gas flow from one region to the next. Also, the seal has inlet and outlet vent holes defined through the honeycomb structure at respective upstream and downstream ends thereof which communicate with correspondingly located ones of the regions. The inlet and outlet vent holes are aligned along respective planes extending radially relative to a longitudinal axis of the engine and the holes are disposed at angles extending in tangential directions along the radial planes.