Volume 33 • Number 2 • 2010   • On the Existence of T-Direction and Nevanlinna Direction of K-Quasi-Meromorphic Mappings Dealing with Multiple Values HongYan Xu and Tang-Sen Zhan Abstract. In this paper, by using Ahlfors' theory of covering surfaces, we prove that for quasi-meromorphic mapping ƒ satisfying there exists at least one T-direction of ƒ dealing with multiple values. We also prove that there exists at least one Nevanlinna direction of ƒ dealing with multiple values which is also T-direction of ƒ dealing with multiple values under the same condition. 2000 Mathematics Subject Classification: 30D60. Full text: PDF