We show that the 2-matrix string model corresponds to a coupled system
of 2 + 1-dimensional KP and modified KP ((m)KP2+1) integrable equatio
ns subject to a specific ''symmetry'' constraint. The latter together
with the Miura-Konopelchenko map for (m)KP2+1 are the continuum incarn
ation of the matrix string equation. The (m)KP2+1 Miura and Backlund t
ransformations are natural consequences of the underlying lattice stru
cture. The constrained (m)KP2+1 system is equivalent to a 1 + 1-dimens
ional generalized KP-KdV hierarchy related to graded SL(3,1). We provi
de an explicit representation of this hierarchy, including the associa
ted W(2,1)-algebra of the second Hamiltonian structure, in terms of fr
ee currents.