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The nuclear shadowing and antishadowing effects are explained by a unitarized BFKL equation.The Q2-and x-variations of the nuclear parton distributions are detailed based on the level of the unintegrated gluon distribution.In particular,the asymptotical behavior of the unintegrated gluon distribution near the saturation limit in nuclear targets is studied. Our results in the nuclear targets are insensitive to the input distributions if the parameters are fixed by the data of a flee proton.