  A $\lambda$-graph system is a labeled Bratteli diagram with certain
additional structure, which presents a subshift. The class of the
$C^*$-algebras $\mathcal{O}_{\frak L}$ associated with the $\lambda$-graph
systems is a generalized class of the class of Cuntz--Krieger algebras. In this
paper, we will compute the strong extension groups
$\operatorname{Ext}_{\operatorname{s}}(\mathcal{O}_{\frak L})$ for the
$C^*$-algebras associated with $\lambda$-graph systems ${\frak L}$ and study
their relation with the weak extension group
$\operatorname{Ext}_{\operatorname{w}}(\mathcal{O}_{\frak L})$.
