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Real-time Ethernet (RTE) technologies are becoming increasingly popular, as they provide high bandwidth and are able to meet the requirements of industrial real-time communications. Among RTE protocols, the EtherCAT standard is suitable for motion control and closed-loop control applications, which require very short cycle times. As EtherCAT was specifically devised for periodic traffic, aperiodic real-time transmissions are far from being efficient, as they entail long cycle times. To overcome this limitation, this paper presents a general framework for priority-driven swapping (PdS)-based scheduling of aperiodic real-time messages over EtherCAT networks, which uniformly covers both dynamic and static priority and allows for very short cycle times. This paper provides a description of the PdS framework, a schedulability analysis for both static priority and dynamic priority scheduling, and simulative assessments obtained through OMNeT++ simulations.