In this paper, the authors first classify all nonoscillatory solutions of equation (1) $${Delta}^2|{Delta}^2{_{y_n}}|^{{alpha}-1}{Delta}^2{_{y_n}}+q_n|y_{{sigma}(n)}|^{{eta}-1}y_{{sigma}(n)}=o,;n{in}mathbb{N}$$ into six disjoint classes according to their asymptotic behavior, and then they obtain necessary and sufficient conditions for the existence of solutions in these classes. Examples are inserted to illustrate the results.