Abstract: The structure of the solution of nonlinear parametric programming problem with a one dimensional parameter is reanalyzed in terms of bifurcational behav-ior of the curves near a critical point of F-J points set, so is the persistence ofminima along these curves. In this paper, generalized results of A.B.Poore and C.A. Thiart are presented, with a numerical method to compute the number ofbifurcational curves in some neighbourhood of the critical point.