A gas turbine engine comprising a transition duct , a vane structure and a seal assembly , wherein the seal assembly is provided between a transition seal structure associated with a downstream end of the transition duct and a vane seal structure associated with an upstream end of the vane structure in a first row vane assembly of the gas turbine engine, the seal assembly comprising: an outer seal structure comprising inner and outer seal members , each seal member having a radially extending first leg and an axially extending second leg that extends transversely from a junction with the first leg to provide each seal member with an L or V-shape, each seal member including a plurality of circumferentially spaced apart notches extending from an edge of at least one of the first and second legs (34A, 36A; 34B, 36B) toward the junction ; wherein: the inner and outer seal members are arranged in a nested relationship with one of the seal members being positioned between the first and second legs (34A, 36A; 34B, 36B) of the other seal member such that the respective junctions of the inner and outer seal members are adjacent to one another; at least one of the first and second legs (34A, 36A; 34B, 36B) of both of the inner and outer seal members is received in a corresponding outer slot defined at least in part by one of the transition seal structure and the vane seal structure ; and the inner and outer seal members are arranged such that at least some of the notches of the inner seal member are not circumferentially aligned with the notches of the outer seal member . an outer seal structure comprising inner and outer seal members , each seal member having a radially extending first leg and an axially extending second leg that extends transversely from a junction with the first leg to provide each seal member with an L or V-shape, each seal member including a plurality of circumferentially spaced apart notches extending from an edge of at least one of the first and second legs (34A, 36A; 34B, 36B) toward the junction ; wherein: the inner and outer seal members are arranged in a nested relationship with one of the seal members being positioned between the first and second legs (34A, 36A; 34B, 36B) of the other seal member such that the respective junctions of the inner and outer seal members are adjacent to one another; at least one of the first and second legs (34A, 36A; 34B, 36B) of both of the inner and outer seal members is received in a corresponding outer slot defined at least in part by one of the transition seal structure and the vane seal structure ; and the inner and outer seal members are arranged such that at least some of the notches of the inner seal member are not circumferentially aligned with the notches of the outer seal member . the inner and outer seal members are arranged in a nested relationship with one of the seal members being positioned between the first and second legs (34A, 36A; 34B, 36B) of the other seal member such that the respective junctions of the inner and outer seal members are adjacent to one another; at least one of the first and second legs (34A, 36A; 34B, 36B) of both of the inner and outer seal members is received in a corresponding outer slot defined at least in part by one of the transition seal structure and the vane seal structure ; and the inner and outer seal members are arranged such that at least some of the notches of the inner seal member are not circumferentially aligned with the notches of the outer seal member . <EOS>