Nonlinear　systems　of　difference　equations　with　delay　and　nonlinearities　of　a　sector　type　are　studied.　New　constructions　of　Lyapunov-Krasovskii　functionals　are　proposed　for　such　sys-tems.　With　the　aid　of　these　functionals,　conditions　are　obtained　under　which　solutions　of　the　considered　systems　are　uniformly　ultimately　bounded　for　any　value　of　delay.　An　example　is　given　to　demonstrate　the　effectiveness　of　the　proposed　approaches.　©　2018　IEEE.