  This paper is devoted to integrability conditions for systems of linear
difference and differential equations with difference parameters. It is shown
that such a system is difference isomonodromic if and only if it is difference
isomonodromic with respect to each parameter separately. Due to this result, it
is no longer necessary to solve non-linear difference equations to verify
isomonodromicity, which will improve efficiency of computation with these
systems.
