In this paper, we study global behavior of the following max-type system of difference equations of the second order with four variables and period-two parameters
{xnβ=max{Anβ,ynβ2βznβ1ββ},Β ynβ=max{Bnβ,xnβ2βwnβ1ββ},Β znβ=max{Cnβ,wnβ2βxnβ1ββ},Β wnβ=max{Dnβ,znβ2βynβ1ββ},Β βΒ Β nβ{0,1,2,β―},
where Anβ,Bnβ,Cnβ,Dnββ(0,+β) are periodic sequences with period 2 and the initial values xβiβ,yβiβ,zβiβ,wβiββ(0,+β)Β (1β€iβ€2). We show that if \min\{A_0C_1, B_0D_1, A_1C_0, B_1D_0\} < 1 , then this system has unbounded solutions. Also, if min{A0βC1β,B0βD1β,A1βC0β,B1βD0β}β₯1, then every solution of this system is eventually periodic with period 4.</p