Business Process Management as a discipline has suffered several changes during the implementation of the execution and monitoring phases in the cloud model. Different strategies have been seen in terms of the implementation needed in order to gather information from the different nodes during process execution, and finally show the results seamlessly without the notion of a partitioned business process. Another aspect to introduce in this context is Process Variability, in terms of the changes suffered by a process model during its lifecycle, and how these changes affect the actual instances in execution. In terms of a cloud BPM implementation, Process Variability adds even more complexity during execution considering the different process portions, as well as during the gathering and monitoring phases. The main purpose of this work is to establish how the different aspects of a cloud BPM implementation with decomposed processes are affected by introducing concepts of Process Variability, both in execution as well as in the monitoring phase. To achieve this goal an analysis of some current bibliography and the main aspects of process variability management is accomplished.