A torsional vibration damper or torsionally elastic coupling comprises an inner portion, an outer portion, and radial leaf spring assemblies extending between the inner and outer portions. Each leaf spring assembly is clamped in a clamping area between adapters at one end of the leaf spring assembly and includes two leaf springs fixed to the outer portion at the one end and having their opposite ends engage in axial grooves of the inner portion. The two leaf springs protrude radially inwards from the clamping area up to the opposite ends engaged in the axial grooves and, to reduce wear phenomena and to improve the load-bearing capacity of the leaf springs for torque transmission, they define a free clearance of movement from the clamping area to the axial grooves.