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

$\Gamma-\Sigma-C^{0}-$determinacy of $\Gamma-\Sigma-C^{0}-$equivariant  bifurcation problems with respect to $\Gamma-\Sigma-C^{0}-$BD and contact  equivalence from the weighted point view