Abstract: A combustor/transition piece for a gas turbine including a double walled structure having a plurality of cooling channels, both axially and, in some cases, circumferential cross-flow passages positioned between the structure's inner member and the outer member to provide cooling air thereto, are formed in the area between the inner member of the combustor and the outer member thereof. The passages preferably extend both axially and circumferentially with respect to the direction of flow through the combustor/transition piece. The axial passages extend completely from one end to the other and the circumferential passages extend around the circumference of the combustor/transition piece. The addition of a circumferential cross-flow passage connecting axial flow coolant passages in double wall turbine components can prevent combustor/transition piece part failure due to axial passage inlet blockage without affecting normal, unblocked cooling.