| In this thesis, the dynamics, i.e., the global asymptotic stability, the periodic characterand the boundedness nature of the solutions, of two classes of difference equations are investigated, and some corresponding results are promoted. This thesis is composed of four chapters.In chapter one, the historic background, the recent development tendence of the differenceequations and the main results of this paper are introduced briefly.In chapter two, some basic definitions and known results of difference equations which will be used in context are introduced.In chapter three, we study the dynamics of the difference equationxn+1=f(xn-k1,xn-k2,…,xn-ks;xn-m1,xn-m2,…,xn-mt,n=0,1,…,where 0≤k1 < k2 <…s and 0≤m1< m2 <…< mt with {k1, k2,…, ks}∩{m1,m2,…, mt} = 0, the initial values are positive. We obtain sufficient conditions under which the positive equilibrium of this equation is globally asymptotically stable, every solution of this equation converges to a periodic soltion, and this difference equation has unbound solutions respectively.In chapter four, we study the dynamics of the difference equationwhere fi,gi∈C((0,∞)k+1, (0,∞)) for i∈{1,…, 2s}and j∈{1,…2t}, h e C([0,∞)k+1, [0,∞)), k∈{1,2,…} and the initial values x-k, x-k+1,…, x0∈(0,∞). We give a sufficient conditionunder which the unique positive equilibrium of this equation is globally asymptotically stable.
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