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The main goal of the technical note is to extend the Mikhaylov criterion to the case of neutral time delay systems. The modification consists in determining the vertex angle that bounds the argument oscillations of the Mikhaylov hodograph at high frequency ranges. Utilizing the strong stability concept, the presented stability criterion is examined from the viewpoint of potential fragility with respect to arbitrarily small delay changes. To facilitate the more demanding argument assessment, the Mikhaylov hodograph is converted to PoincarEacute-like mapping.