A coupling system of an elevator car door drive includes a traction device, at least one coupling unit coupled to the traction device, and an adapter element which has a first interlocking adjustment structure which, together with interlocking elements of the traction device, forms a first interlocking unit that secures a relative position of the adapter element with respect to the traction device, which relative position can be adjusted in defined interlocking adjustment positions. The coupling unit has a second interlocking unit which secures a relative position of the adapter element with respect to the coupling unit, which relative position can be adjusted in defined interlocking adjustment positions, wherein, in the second interlocking unit, the distance between directly adjacent interlocking adjustment positions is smaller than the distance between directly adjacent interlocking adjustment positions of the first interlocking unit.