Apparatus for oxygenating blood including a diffusion device 12 incorporating a folded semi-permeable membrane and a heat exchange device 54 connected together for flow of blood through both devices, a rigid reservoir 78 being provided for receiving blood from the heat exchange device, the blood circuit defined by the diffusion device, heat exhange device and reservoir being of substantially constant width perpendicular to the general flow of blood through the apparatus. A stiff thermoplastic coated backing material has lateral tabs folded back against the remainder of the backing and heat sealed to provide a spacing and gasket seal at opposed edges of the stack. <IMAGE>
