Method and system for monitoring a connection between two terminal equipment items, corresponding computer program product

A method is proposed for monitoring a connection between end devices via a communications network. A set of modes having at least two monitoring modes and a ranking order associated with the set of modes, are agreed upon between the end devices and a network device present on a path between the end devices. The method includes an activation of the set of modes, corresponding to an activation of the first mode according to the ranking order; then an activation, according to the ranking order, of each other mode of the set of modes. Each monitoring mode includes at least one mechanism implemented by at least one of the end devices and enabling the network device to perform at least one function of monitoring the connection.