Pham Hoang Ha (Hanoi National University of Education), Introduction, The unicity theorems with truncated multiplicities of meromorphic mappings of into, the complex projective space sharing a finite set of q fixed hyperplanes in have, received much attention in the last few decades, and they are related to many problems in, Nevanlinna theory and hyperbolic complex analysis (see the reference in [A], [TQ1], [TQ2], [DT1], [DT2], [DT3] for the development in related subjects). In the case where multiplicities, truncated by 1 or 2, the first results due to H. Fujimoto [Fu] and, L. Smiley [S] when q 3N+2, and the recent results due to Thai!Quang [TQ2] and Dethloff!, Tan [DT1], [DT2] when 3N'1 q 3N+1., How to say about the unicity theorems with truncated multiplicities in the case where

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