This paper concerns noncausal, nonlinear discrete singular systems of the form
![aX_{k+1} + Bx_{k} = m[x]_{k}](/images/tex/3493.gif)
on the infinite interval
![i = [0, 1, --.]](/images/tex/3494.gif)
for some causal, nonlinear time variable operators

. Existence theorems for bounded solutions are given. Methods for estimating the infinite time problem by a finite time problem are developed.