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For an analytic variety V in ℂⁿ containing the origin which satisfies the local Phragmén-Lindelöf condition $P{L}_{loc}\left(0\right)$ it is shown that for each real simple curve γ and each d ≥ 1 the limit variety $T_{\gamma ,d}V$ satisfies the strong Phragmén-Lindelöf condition (SPL).