Abstract. In this paper, we study entire solutions of some nonlineardifference equations and transcendental meromorphic solutons of somenonlinear differential equations. Our results generalize the results due to[11], [17]. 1. Introduction and mainresultWe assume that the reader is familiar with the standard notations and fun-damental results in Nevanlinna theory. For example, we use the followingnotations in value distribution such as T(r,f), m(r,f), N(r,f), S(r,f), whereas usual S(r,f) denotes any quantity satisfying S(r,f) = o{T(r,f)} as r → ∞outside a possible exceptional set of finite logarithmic measure. We refer thereader to the books [3, 6], and [7]. For an element η in complex plane C, we willuse f(z +η) and ∆ η f(z) := f(z +η) −f(z) to denote the shift and differenceof f(z) respectively.As we know, Nevanlinna theory is an efficient tool in the research of complexdifferential theory. It is interesting to use the Nevanlinna theory to studycomplex equation of various types. Many results about complex differenceequations (cf. [1, 2, 4, 5]), complex differential equations (cf. [14]) or complexdifferential-difference equations (cf. [10], [12] and [15]) were rapidly obtained,respectively.In 2004, Yang and Li [15] studied some certain types of nonlinear equations,and proved the following results.TheoremA([15]). Take a positive integer n. Let a,b