  The conservation laws for a class of nonlinear equations with variable
coefficients on discrete and noncommutative spaces are derived. For discrete
models the conserved charges are constructed explicitly. The applications of
the general method include equations on quantum plane, supersymmetric equations
for chiral and antichiral supermultiplets as well as auxiliary equations of
integrable models - principal chiral model and various cases of nonlinear Toda
lattice equations.
