  Results of a calculation valid to all orders in the nuclear-strength
parameter Z\alpha are presented for the two-loop Lamb shift, notably for the
two-loop self-energy correction, for the ground and first excited states of
ions with the nuclear charge numbers Z=60-100. A detailed comparison of the
all-order calculation with earlier investigations based on an expansion in the
parameter Z\alpha is given. The calculation removes the largest theoretical
uncertainty for the 2p_j-2s transition energies in heavy Li-like ions and is
important for interpretation of experimental data.
