In this paper, we deal with the form and the periodicity of the solutions of the max-type system of difference equations u n + 1 = max A n / v n − 1 , u n − 1 , v n + 1 = max B n / w n − 1 , w n + 1 = max C n / u n − 1 , w n − 1 where the initial conditions u − 1 , u 0 ∈ 0 , ∞ , v − 1 , v 0 ∈ 0 , ∞ , w − 1 , w 0 ∈ 0 , ∞ and A n n ∈ N 0 , B n n ∈ N 0 , C n n ∈ N 0 are positive two-periodic sequences.