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In this paper, we construct center stable manifolds around unstable linesolitary waves of the Zakharov--Kuznetsov equation on two dimensionalcylindrical spaces with $2\pi L$ period. In the previous paper, center stablemanifolds around unstable line solitary waves have been constructed withoutcritical speed $c =4n^2/5L^2$ for positive integer $n>1$. Since the linearizedoperator around line solitary waves with critical speed is degenerate, we provethe stability condition of the center stable manifold for critical speed byapplying to the estimate of 4th order term of a Lyapunov function.

Center stable manifolds around line solitary waves of the Zakharov--Kuznetsov equation with critical speed