A thermodynamic approach for analyzing the structural stability of process plants is presented. The results are connected with a theory of systems described by dynamic conservation balances using a potential for stability analysis that generalizes the availability/exergy. This theory is used to show that interconnected systems with no source terms and Kirchhoff convection are structurally asymptotically stable. The approach is applicable for systems where only Kirchhoff convective transport and transfer processes with equilibrium take place. Systems with constant mass holdup in every balancing volume satisfy the condition of Kirchhoff convection. The general results are illustrated in examples of practical importance including heat exchanger networks, multicomponent flash, and multicomponent distillation with constant molar flows.