We formulate the constrained KP hierarchy (denoted by cKP(K+1,M)) as a
n affine <(sl)over cap>(M + K + 1) matrix integrable hierarchy general
izing the Drinfeld-Sokolov hierarchy. Using an algebraic approach, inc
luding the graded structure of the general ized Drinfeld-Sokolov hiera
rchy, we are able to find several new universal results valid for the
cKP hierarchy. In particular, our method yields a closed expression fo
r the second bracket obtained through Dirac reduction of any untwisted
affine Kac-Moody current algebra. An explicit example is given for th
e case <(sl)over cap>(M + K + 1), for which a closed expression for th
e general recursion operator is also obtained. We show how isospectral
flows are characterized and grouped according to the semisimple non-r
egular element E of sl(Mf K + 1) and the content of the center of the
kernel of E. (C) 1997 American Institute of Physics.