  Updated rerefences and introduction. Given a knot in an integer homology
sphere, one can construct a family of closed 3-manifolds (parametrized by the
positive integers), namely the cyclic branched coverings of the knot. In this
paper we give a formula for the the Casson-Walker invariants of these
3-manifolds in terms of residues of a rational function (which measures the
2-loop part of the Kontsevich integral of a knot) and the signature function of
the knot. Our main result actually computes the LMO invariant of cyclic
branched covers in terms of a rational invariant of the knot and its signature
function. Revised version.
