A filter system has a primary filter element and a secondary filter element arranged in a housing between fluid inlet and fluid outlet. The secondary filter element is arranged inside the primary filter element. The primary and secondary filter elements are flowed through sequentially by a fluid to be filtered. The secondary filter element contains an adsorption agent and has a coupling device. The housing has a coupling element at the fluid outlet for coupling to the coupling device. The secondary filter element has a filter medium body which extends along a longitudinal axis and surrounds a hollow interior. The coupling device is arranged at an open end of the filter medium body and configured to be coupled rotationally fixed to the primary filter element. The coupling device has a thread for engaging a thread of the coupling element of the housing complementary to the thread of the coupling device.