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This paper is concerned with delayed generalized 2D discrete logistic systems of the form xm+1,n=f(m,n,xm,n,xm,n+1,xm−Ã,n−Ä) , where à and Ä are positive integers, f:ℕ02×â„Â3→℠is a real function, which contains the logistic map as a special case, and m and n are nonnegative integers, where ℕ0={0,1,…} and â„Â=(−∞,∞). Some sufficient conditions for this system to be stable and exponentially stable are derived.