An arrangement is provided for statically sealing between the inner shroud 12 of individual stator vanes of a gas turbine, and a seal housing 14 provided with a radially outwardly open channel 22 into which is received a plurality of outer seal segments 24, and which includes a radially outwardly open channel 33 throughout the length of each outer seal segment and with a plurality of inner seal segments received in the channel, with the outer seal segments being biased outwardly by the springs 36, and the inner seal segments 34 being biased outwardly into sealing contact with individual inner shrouds by the concentric inner compression springs 38 carried by the outer seal segments 24.