  We consider the operation of Whitehead double on a component of a link and
study the behavior of Milnor invariants under this operation. We show that this
operation turns a link whose Milnor invariants of length < k are all zero into
a link with vanishing Milnor invariants of length < 2k, and we provide formulas
for the first non-vanishing ones.
  As a consequence, we obtain statements relating the notions of link-homotopy
and self Delta-equivalence via the Whitehead double operation. By using our
result, we show that a Brunnian link L is link-homotopic to the unlink if and
only if a link L with a single component Whitehed doubled is self
Delta-equivalent to the unlink.
