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Lion's share of cloud research has been focusing on performance related problems. However, cloud computing will also change the way in which business processes are managed and supported, e.g., more and more organizations will be sharing common processes. In the classical setting, where product software is used, different organizations can make ad-hoc customizations to let the system fit their needs. This is undesirable, especially when multiple organizations share a cloud infrastructure. Configurable process models enable the sharing of common processes among different organizations in a controlled manner. This paper discusses challenges and opportunities related to business process configuration. Causal nets (C-nets) are proposed as a new formalism to deal with these challenges, e.g., merging variants into a configurable model is supported by a simple union operator. C-nets also provide a good representational bias for process mining, i.e., process discovery and conformance checking based on event logs. In the context of cloud computing, we focus on the application of C-nets to cross-organizational process mining.