It is generally agreed that the Bordoni relaxation in fcc metals is caused by kink-pair formation in dislocations along close-packed lattice directions. None of the existing theoretical treatments using the line tension approach is however able to give an adequate description of this process. The bow-out of a segment must be described by a kink-chain, and its configuration is essentially controlled by the interaction energy of the kinks. This coordinate-space is multi-dimensional depending on the number n of the kinkpairs, their positions and their widths. When the kinks have high mobility (as expected in fcc metals) and assume equilibrium positions with respect to stress, the dimensions of the coordinate-space are reduced to two. The system in mechanical equilibrium can then be described by its enthalpy H( , n), which generally can only be obtained by numerical methods. For each stress a number of mechanically stable configurations with different number n of kink-pairs exist. Thermodynamic equilibrium is the reached in the ground state, i.e. the state with lowest enthalpy H with an equilibrium number n( ) of kink-pairs. The energy dissipation is caused by a phase-lag between (t) and n(t) in the neighbourhood of n. The generalized ParΓ© condition does not apply for multiple kink-pairs and for an oscillating stress, even small, there are practically always a number of states accessible with different number of kink-pairs. For shallow bow-outs analytical solutions for H( , n) exist. It is then possible to derive the magnitude of the energy dissipation by numerically integrating the differential equation for the dislocation velocity. An essential role plays the asymmetry in the dislocation movement: The forward movement must always take place by thermally activated kink-pair nucleation, whereas the backward movement against a still positive stress will occur by kink-pair collapse, for which the energy barriers can be smaller. Due to the dissociation of dislocations in fcc lattices into two partials, a distribution of activation energies is expected.