In this paper, we obtain a new sufficient condition for oscillation of all solutions of the system of difference equations of the form

where  are sequences of real numbers,  is an increasing sequence of integers such that

 for all  and

and  is the forward difference operator.

Next, we obtain a new sufficient condition for oscillation of all solutions of the system of neutral difference equations of the form

where  and  is an increasing sequence of integers such that

 for all

Examples illustrating the results are given.