  We study the large time behaviour of the Fisher-KPP equation $\partial$ t u =
$\Delta$u + u -- u 2 in spatial dimension N , when the initial datum is
compactly supported. We prove the existence of a Lipschitz function s of the
unit sphere, such that u(t, x) converges, as t goes to infinity, to U c * |x|
-- c * t + N + 2 c * lnt + s $\infty$ x |x| , where U c * is the 1D travelling
front with minimal speed c * = 2. This extends an earlier result of
G{\"a}rtner.
