NEW THEORIES IN 6 DIMENSIONS AND MATRIX DESCRIPTION OF M-THEORY ON T-5 AND T-5 Z(2)/

We present four infinite series of new quantum theories with super-Poi ncare symmetry in six dimensions, which are not local quantum field th eories. They have string like excitations but the string coupling is o f order one. Compactifying these theories on T-5 we find a Matrix theo ry description of M theory on T-5 and on T-5/Z(2), which is well defin ed and is manifestly U-duality invariant. (C) 1997 Elsevier Science B. V.