We investigate in this paper the solutions and the periodicity of the following rational systems of difference equations of three‐dimensional
xn+1=ynxn−2xn−2±zn−1,yn+1=znyn−2yn−2±xn−1,zn+1=xnzn−2zn−2±yn−1,
with initial conditions x−2,x−1,x0,y−2,y−1,y0,z−2,z−1andz0 are nonzero real numbers. Copyright © 2015 John Wiley & Sons, Ltd.