The authors investigate asymptotic and oscillatory properties of solutions of the neutral second order difference equation with maxima
where are nonnegative integers and , under some restrictions on the sequences . A typical result is the following statement.
Suppose that , and . Then every bounded nonoscillatory solution of (*) satisfies .
Examples illustrating the general results of the paper are given. No comparison of the results and methods of the paper with those concerning the continuous counterpart of (*) are presented.