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Under some conditions, we relate the critical points of $g$ on the real Milnor fibre $X \\cap f^{-1}(\\delta) \\cap B_\\epsilon$, $0 <| \\delta | \\ll \\epsilon \\ll 1$, to the topology of this fibre and other related subanalytic sets. As an application, when $g$ is a generic linear function, we obtain an \"asymptotic\" Gauss-Bonnet formula for the real Milnor fibre of $f$. 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