Telemedicine involves the integration of information, human-machine, and healthcare technologies. Because different modalities of patient care require applications running on heterogeneous computing environment, software interoperability is a major issue in telemedicine. Software agent technology provides a range of promising techniques to solve this problem. This article discusses the development of a methodology for the design of interoperable telemedicine systems (illustrated with a tele-electrocardiography application). Software interoperability between different applications can be modeled at different levels of abstraction such as physical interoperability, data-type interoperability, specification-level interoperability, and semantic interoperability. Software agents address the issue of software interoperability at semantic level. A popular object-oriented software development methodology - unified modeling language (UML) - has been used for this development. This research has demonstrated the feasibility of the development of agent-based interoperable telemedicine systems. More research is needed before widespread deployment of such systems can take place.