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This brief analyzes the linear profiles presented by certain classes of bifurcation indices with respect to the variation of the loading parameter in power systems. The bifurcation indices discussed here are used in practice to predict proximity to saddle-node and some types of limit-induced bifurcations, given their special profiles. Thus, the linearity of these indices is studied with the help of a simple generic test system. Local analyses and observations are also presented and discussed for realistic power-system models.