Injection device having a longitudinal axis, comprising: - a housing for receiving a product container, the product container having a fixedly connected injection needle, a needle protection cap being detachably arranged on the product container, which needle protection cap encloses the injection needle and seals the injection needle in a sterile manner, - a cap, which is detachably provided at a distal end of the housing, - the cap comprising an engagement element in order to cause the needle protection cap to be removed from the product container when the cap is removed from the injection device, - the engagement element being arranged in a rotationally fixed manner relative to the housing, - the cap comprising a rotary sleeve, the rotary sleeve having received the engagement element at least in part, and the rotary sleeve being rotatable relative to the housing and relative to the engagement element about the longitudinal axis, and the rotary sleeve being arranged in an axially fixed manner relative to the engagement element, - the rotary sleeve and the housing each having an undulating or curved guide slot (3b; 1a) which are designed and interact in such a way that the rotary sleeve is rotatable relative to the housing about the longitudinal axis and the rotary sleeve and the engagement element can be moved axially in the distal direction relative to the housing, characterized in that - the rotary sleeve has an anti-reverse-rotation element and the engagement element or the housing has an anti-reverse-rotation counter element in order to allow a rotation of the rotary sleeve in one direction and to block a rotation of the rotary sleeve in the opposite direction. - a housing for receiving a product container, the product container having a fixedly connected injection needle, a needle protection cap being detachably arranged on the product container, which needle protection cap encloses the injection needle and seals the injection needle in a sterile manner, - a cap, which is detachably provided at a distal end of the housing, - the cap comprising an engagement element in order to cause the needle protection cap to be removed from the product container when the cap is removed from the injection device, - the engagement element being arranged in a rotationally fixed manner relative to the housing, - the cap comprising a rotary sleeve, the rotary sleeve having received the engagement element at least in part, and the rotary sleeve being rotatable relative to the housing and relative to the engagement element about the longitudinal axis, and the rotary sleeve being arranged in an axially fixed manner relative to the engagement element, - the rotary sleeve and the housing each having an undulating or curved guide slot (3b; 1a) which are designed and interact in such a way that the rotary sleeve is rotatable relative to the housing about the longitudinal axis and the rotary sleeve and the engagement element can be moved axially in the distal direction relative to the housing, characterized in that - the rotary sleeve has an anti-reverse-rotation element and the engagement element or the housing has an anti-reverse-rotation counter element in order to allow a rotation of the rotary sleeve in one direction and to block a rotation of the rotary sleeve in the opposite direction.