An assembly for a drug delivery device is provided comprising a screw member comprising a thread, the thread including at least two consecutive portions, the portions having different leads. The device further includes a nut member. The assembly is configured such that, in a first portion of the thread, the nut member includes a first position with respect to an axis transversal to the rotational axis and in a second portion of the thread, the nut member includes a second position with respect to the axis transversal to the rotational axis. The nut member is configured to perform a tilting movement from the first position into the second position when the nut member passes from the first portion to the second portion. Furthermore, a drug delivery device comprising the assembly is described.