The notion of lp trichotomy for a linear difference system is here considered as extension of exponential trichotomy and lp dichotomy. The main properties are analyzed and necessary and sufficient conditions for the existence are given. The asymptotic behavior of solutions of a quasilinear system x(n + 1) = A(n)x(n) + f(n; x(n)) is studied under the assumption that the associated linear system possesses a lp trichotomy.