In a previous paper (Presentations of subshifts and their topological conjugacy invariants. Doc. Math.4 (1999), 285–340), the notion of $\lambda$-graph system has been introduced. The $\lambda$-graph systems are generalizations of finite directed labeled graphs. In this paper, we study periodic points of $\lambda$-graph systems. We introduce some invariants for a $\lambda$-graph system $\mathfrak L$ to count the cardinal number of $p$-periodic points of $\mathfrak L$. They are invariant under strong shift equivalence of $\lambda$-graph systems. We then consider the zeta functions of $\lambda$-graph systems, which are also invariant under strong shift equivalence of $\lambda$-graph systems. Some examples are also presented.