An apparatus is provided for producing and/or disengaging a fluid flow-capable medical threaded connection. The connection can be a Luer lock connection. The apparatus includes a first receiving device for receiving a first connecting element, and a second receiving device for receiving a second connecting element. The first receiving device and the second receiving device are rotatable relative to each other about a common screwing axis, and displaceable relative to each other along the screwing axis. The apparatus is designed to relatively move the first receiving device and the second receiving device toward and away from each other such that the first connecting element and the second connecting element can be screwed together or disengaged. An associated connecting element can be introduced into the first receiving device and/or into the second receiving device, in a radial direction relative to the screwing axis. A method is also provided.