A component of a turbine stage of a gas turbine engine, the component forming an endwall for the working gas annulus of the stage, and the component having one or more internal passages behind the endwall which, in use, carry a flow of cooling air providing convective cooling for the component at the endwall, wherein: each passage is formed by a plurality of straight passage sections (50a, 50b, 50c) which connect in end-to-end series to provide a single flow path such that the connections between nearest-neighbour passage sections form successive 90° angled bends; a first portion of the passage sections lies in a first plane, a second portion of the passage sections lies in a second plane which is spaced from and parallel to the first plane, and a third portion of the passage sections extends perpendicularly between the first and the second planes; the first plane and the second plane are both spaced from and parallel to a gas washed plane of the endwall; the passage sections (50a, 50b, 50c) are either of square, rectangular, or circular cross-section, and the passage follows a convoluted path where each passage section extends parallel to one of three axes (X, Y, Z), the first and second axes (X, Y) being parallel to the first and second planes, and the third axis being perpendicular to the first and the second planes; and, characterised in that the passage sections repeat themselves every six passage sections, where every group of three successive end-to-end connected passage sections has one passage section extending along each of the axes; or in that the passage sections repeat themselves every eight passage sections, where every group of four successive end-to-end connected passage sections has at least one passage section which extends along each of the axes, with only one passage section in each of these groups extending parallel to the direction of overall extension of the passage. each passage is formed by a plurality of straight passage sections (50a, 50b, 50c) which connect in end-to-end series to provide a single flow path such that the connections between nearest-neighbour passage sections form successive 90° angled bends; a first portion of the passage sections lies in a first plane, a second portion of the passage sections lies in a second plane which is spaced from and parallel to the first plane, and a third portion of the passage sections extends perpendicularly between the first and the second planes; the first plane and the second plane are both spaced from and parallel to a gas washed plane of the endwall; the passage sections (50a, 50b, 50c) are either of square, rectangular, or circular cross-section, and the passage follows a convoluted path where each passage section extends parallel to one of three axes (X, Y, Z), the first and second axes (X, Y) being parallel to the first and second planes, and the third axis being perpendicular to the first and the second planes; and, characterised in that the passage sections repeat themselves every six passage sections, where every group of three successive end-to-end connected passage sections has one passage section extending along each of the axes; or in that the passage sections repeat themselves every eight passage sections, where every group of four successive end-to-end connected passage sections has at least one passage section which extends along each of the axes, with only one passage section in each of these groups extending parallel to the direction of overall extension of the passage.