We propose a new integrable N = 2 supersymmetric Toda lattice hierarch
y which may be relevant for constructing a supersymmetric one-matrix m
odel. We define its first two Hamiltonian structures, the recursion op
erator and Lax-pair representation. We provide partial evidence for th
e existence of an infinite-dimensional N = 2 superalgebra of its flows
. We study its bosonic limit and introduce new Lax-pair representation
s for the bosonic Toda lattice hierarchy. Finally we discuss the relev
ance this approach for constructing N = 2 supersymmetric generalized T
oda lattice hierarchies. (C) 1998 Elsevier Science B.V.