The paper describes the different phases and subdomains of process modelling and their needs for conceptual and linguistic support, and in what forms. We group the relevant factors into three dimensions: meta-process phases, process elements, and the tool/user views. In the first dimension, we focus on enactable process models. For such models, we describe the design alternatives for a core process modelling language and a set of tailored sub-languages to cover special process elements. However, no detailed and functional comparison of possible modelling language are attempted. Then we address interoperability between related sub-models and its implication to the language design. We also present a general architecture for a Process-Centered Software Engineering Environment, with a segmented repository of model servers. Some concrete language realisations, mainly from the EPOS PSEE, are used throughout the presentation. We also give a realistic example of the design of an interoperabl...