ON A SYSTEM OF RATIONAL DIFFERENCE EQUATIONS xn+1 =

xn−1 yn xn−1−1, yn+1 = yn−1 xn yn−1−1, zn+1 = 1 yn zn−1 Abstract. In this paper, we are concerned with a three- dimen-sional system of rational difference equations. We present solu-tions of the system in an explicit way and obtain the asymptotical behavior of solutions according to initial values. We also give suf-ficient conditions of existing four-period solutions