  In this paper, $C^{0}$ finite determination of $\Gamma-$equivariant
bifurcation problems in the relative case from the weighted point view is being
discussed . Some criteria on the $C^{0}$ finite determination of
$\Gamma-$equi-variant bifurcation problems in the relative case are then
obtained in terms of an analytic-geometric non-degeneracy condition, which
generalize the result on the $C^{0}$ finite determination of bifurcation
problems given by P.B.Percell and P.N.Brown.
