The exactly integrable systems connected with a semisimple series A for arb
itrary grading are presented in an explicit form. Their general solutions a
re expressed in terms of the matrix elements of various fundamental represe
ntations of the A, groups. The simplest example of such systems is the gene
ralized Toda chain with matrices of arbitrary dimensions in each point of t
he lattice. (C) 1999 Published by Elsevier Science B.V.