(eng): Stability of interconnection of two or several dynamical systems is a crucial property that needs to be satis ed. The small gain theorem has been recognized as an effective tool for guaranteeing stability of interconnection of dynamical systems, even for systems with time delays. In this contribution, the small gain theorem for connection of systems described by quasilinear parabolic equations is investigated. Conditions guaranteeing Lyapunov stability for the interconnenction of two such systems are derived. This is achieved by introducing a Lyapunov function de ned on a suitable Sobolev space. Attention is also paid to time-delay systems. Here, the stability of the interconnection of systems is demonstrated using a generalization of the Lyapunov-Krasovskii od Lyapunov-Razumikhin fucntionals to systems, again de ned on a Sobolev space. The results are illustrated by numerical simulations.