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We give various examples of asymmetric orbifold models to possessintertwining currents which convert untwisted string states to twisted ones,and vice versa, and see that such asymmetric orbifold models are severelyrestricted. The existence of the intertwining currents leads to the enhancementof symmetries in asymmetric orbifold models.Comment: 25page

String Theories on the Asymmetric Orbifolds with Twist-Untwist Intertwining Currents