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The Zee model is one of promising models of neutrino mass generation mechanism. However, the original Zee model is not on the framework of the ground unification scenario, and moreover, it is recently pointed out that the predicted value of must be satisfied the relation . We discuss whether possible GUT versions of the Zee model can be free from the severe constraint $\sin^2 2\theta_{solar}
0.99$ or not. We will conclude that the following two models are promising: an R-parity violating SUSY GUT model and an SO(10) model with a 126-plet scalar.

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