A conductor clamp (4) for a trailing line (5) which is secured to crabs (7) which can be moved along a carrier rail (1) comprises a support (8) for the trailing line, a clamping device (9) for securing the trailing line to the support and a shock absorber (10) for absorbing an impact of the first crab on the conductor clamp. The shock absorber has at least two spring bodies (20, 22) which have different characteristics and which are arranged one behind the other in the anticipated direction of action of the shock absorber. In this context, the most resilient spring body (20) is arranged closest to the end of the shock absorber which is provided for the application of an impact force. The shock absorber also has a lifting rod (16) which can be displaced under the effective impact force in the anticipated direction of action of the shock absorber. At the two ends of the lifting rod, spring bodies with different characteristics are arranged. The shock absorber has a housing in which the lifting rod is movably mounted, with an internal end of the lifting rod being located inside the housing, and an external end of said lifting rod being located outside the housing.