This paper considers the internal stability of an interconnection of two implicit systems based on passivity theory. The passivity for implicit systems is defined as a generalization of the passivity in the traditional input-output framework. We derive a necessary and sucient condition for the passivity of an implicit system in terms of a constrained linear matrix inequality (CLMI). Based on this CLMI condition, we derive a sufficient condition for the internal stability of an interconnection of two implicit systems.