  We study almost automorphic solutions of the discrete delayed neutral dynamic
system% \[ x(t+1)=A(t)x(t)+\Delta Q(t,x(t-g(t)))+G(t,x(t),x(t-g(t))) \] by
means of a fixed point theorem due to Krasnoselskii. Using discrete variant of
exponential dichotomy and proving uniqueness of projector of discrete
exponential dichotomy we invert the equation and obtain some limit results
leading to sufficient conditions for the existence of almost automorphic
solutions of the neutral system. Unlike the existing literature we prove our
existence results without assuming boundedness of inverse matrix $A\left(
t\right) ^{-1}$. Hence, we significantly improve the results in the existing
literature. We provide two examples to illustrate effectiveness of our results.
Finally, we also provide an existence result for almost periodic solutions of
the system.
