We report the detections of the anticorrelated soft and hard X-rays, and the time lags of $hectosecond from the neutron star low-mass X-ray binary Cyg X-2, a well-known Z-type luminous source. Both anticorrelation and the positive correlation were detected during the low-intensity states, while only the latter showed up during highintensity states. Comparing with the lower part of normal branch and flaring branch, we find that more observations located on the horizontal and the upper normal branches are accompanied with anticorrelation, implying the occurrence of the anticorrelation when there is a low mass accretion rate. So far anticorrelated hard lags of 1000 s timescale are only reported from Galactic black hole candidates in their hard states. Here we provide the first evidence that a similar feature can also be established in neutron star systems such as Cyg X-2. Finally, the possible origins of the observed time lags are discussed under current LMXB models.

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