An injection device (30) features a housing (42, 52) for reception of a container (34) having a fluid (32) to be injected, a first element (94) for ejecting injection fluid (32) from such a container (34), and said first element (94) has an external thread (92). A metering element (66, 88) has an internal thread (90) that is in engagement with the external thread (92) of the first element (94), and said metering element (66) is rotatable, together with the first element (94), for preselection of a desired injection dose. A coupling arrangement (K1) serves, during an injection operation, to create a nonrotatable connection between the first element (94) and the housing (42, 52) and thereby to block, during an injection operation, a rotation of the first element (94) relative to the housing (42, 52) but to enable a rotation of the metering element (66, 88) relative to the housing (42, 52).