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Our experimental results show that in Li$_2$Co(WO$_4$)$_2$ a short-range antiferromagnetic (AFM) correlations appear near $\\chi$$_{max}$ $\\sim$ 11 K and two successive long-range AFM phase transitions are observed at T$_{N1}$$\\sim$ 9 K and T$_{N2}$$\\sim$ 7 K. 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