  A generalized Toda Lattice equation is considered. The associated linear
problem (Lax representation) is found. For simple case N=3 the $\tau$-function
Hirota form is presented that allows to construct an exast solutions of the
equations of the 1DGTL. The corresponding hierarchy and its relations with the
nonlinear Schrodinger equation and Hersenberg ferromagnetic equation are
discussed.
