A gas turbine engine comprising: a compressor section and a turbine section, said turbine section including at least one rotor and at least one blade extending radially outwardly from said rotor to a radially outer tip; a blade outer air seal (104;162;170) positioned radially outwardly of said radially outer tip of said blade, said blade outer air seal (104;162;170) having forward and aft hooks (106,108), and said forward and aft hooks (106,108) being supported on forward and aft seal hooks (112,114) of an attachment block; and said attachment block having a forward case mount hook and an aft case mount hook, and said attachment block being supported on a forward case hook and an aft case hook of a static casing within the engine, and said forward case mount hook and said aft case mount hook on said attachment block facing in a first common axial direction, and said forward case hook and said aft case hook facing in a second common axial direction which is opposed to said first common axial direction; wherein there are a plurality of blade outer air seals (104; 162; 170) mounted within said casing; and characterised by there being wedge seals spanning a circumferential gap between adjacent ones of said plurality of blade outer air seals; and in that said wedge seals include portions positioned radially inward of said forward and aft seal hooks (112,114) of said attachment block, and there being stops formed on said wedge seal circumferentially between said forward and aft hooks (106,108) of said blade outer seals (104;162;170), each stop adjacent a respective one of the forward and aft hooks (106,108). a compressor section and a turbine section, said turbine section including at least one rotor and at least one blade extending radially outwardly from said rotor to a radially outer tip; a blade outer air seal (104;162;170) positioned radially outwardly of said radially outer tip of said blade, said blade outer air seal (104;162;170) having forward and aft hooks (106,108), and said forward and aft hooks (106,108) being supported on forward and aft seal hooks (112,114) of an attachment block; and said attachment block having a forward case mount hook and an aft case mount hook, and said attachment block being supported on a forward case hook and an aft case hook of a static casing within the engine, and said forward case mount hook and said aft case mount hook on said attachment block facing in a first common axial direction, and said forward case hook and said aft case hook facing in a second common axial direction which is opposed to said first common axial direction; wherein there are a plurality of blade outer air seals (104; 162; 170) mounted within said casing; and characterised by there being wedge seals spanning a circumferential gap between adjacent ones of said plurality of blade outer air seals; and in that said wedge seals include portions positioned radially inward of said forward and aft seal hooks (112,114) of said attachment block, and there being stops formed on said wedge seal circumferentially between said forward and aft hooks (106,108) of said blade outer seals (104;162;170), each stop adjacent a respective one of the forward and aft hooks (106,108).