This paper introduces the new class of incrementally port-Hamiltonian systems. This class can be obtained from standard port-Hamiltonian systems by replacing the composition of the Dirac structure and energy-dissipating relation by a maximal monotone relation. After introducing this new class of systems, we study their compositions and show that incrementally port-Hamiltonian systems are closed under composition. Also, we study existence and uniqueness os state trajectories for such systems as well as an energy-based state re-initialization principle.