High-level Petri net classes are suited to specify concurrent processes with emphasis both in control and data processing, making them appropriate to specify distributed embedded systems (DES). Embedded systems components are usually synchronous, which means that DES can be seen as Globally-Asynchronous Locally-Synchronous (GALS) systems. This paper proposes to include in high-level Petri nets a set of concepts already introduced for low-level Petri nets allowing the specification of GALS systems, namely time domains, test arcs and priorities. Additionally, this paper proposes external messages and three types of (high-level) asynchronous communication channels, to specify the interaction between distributed components based on message exchange. With these extensions, GALS-DES can be specified using high-level Petri nets. The resulting models include the specification of each component with well-defined boundaries and interface, and also the explicit specification of the asynchronous interaction between components. These models will be used not only to specify the system behavior, but also to be the input for model-checking tools (supporting its verification) and automatic code generation tools (supporting its implementation in software and hardware platforms), giving a contribution to the model-based development approach and hardware-software co-design of DES based on high-level Petri nets.