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This paper proves the global existence of strong solutions of the 2D liquid crystal model when ν1 = k2 = 0, ν2 = k1 = 1 or ν1 = k2 = 1, ν2 = k1 = 0. We also prove some regularity criteria when ν1 = k1 = 1, ν2 = k2 = 0 or ν1 = k1 = 0, ν2 = k2 = 1.