Subject to some conditions, the input data for the Drinfeld-Sokolov
construction of KdV type hierarchies is a quadruplet (\A,\Lambda, d_1, d_0),
where the di are Z-gradations of a loop algebra \A and \Lambda\in \A
is a semisimple element of nonzero d1-grade. A new sufficient condition on
the quadruplet under which the construction works is proposed and examples are
presented. The proposal relies on splitting the d1-grade zero part of \A
into a vector space direct sum of two subalgebras. This permits one to
interpret certain Gelfand-Dickey type systems associated with a nonstandard
splitting of the algebra of pseudo-differential operators in the
Drinfeld-Sokolov framework.Comment: 19 pages, LaTeX fil