A fitting connection for a capillary has a sealing bushing, a compression bushing, and a backing bushing. The backing bushing has a bore for receiving the sealing bushing and the compression bushing into the backing bushing, and the sealing bushing and the compression bushing are each provided with a central bore for feeding through a capillary tube. The bore of the backing bushing has a partly slightly conical bore end which compacts the sealing bushing such that the bore of the sealing bushing exerts a radial surface pressure onto the external wall of the capillary.