Processes are running everywhere. Understanding and analyzing business and software processes and their interactions is critical if we wish to improve them. There are many event logs generated from Information Systems and applications related to fraud detection, healthcare processes, e-commerce processes, and others. These event logs are the starting point for process mining. Process mining aims to discover, monitor, and improve real processes by extracting knowledge from event logs available in information systems. Process mining provides fact-based insight from real event logs that helps analyze and improve existing business processes by answering, for example performance or conformance questions. As the number of applications developed in a cloud infrastructure (often called Software as a Service – SaaS at the application level) is increasing, it becomes essential and useful to study and discover these processes. However, SaaS applications bring new challenges to the problem of process mining. Using the Design Science Research Methodology, this thesis introduces a new method to study, discover, and analyze cloud-based application processes using process mining techniques. It explores the applications and known challenges related to process mining in cloud applications through a systematic literature review (SLR). It then contributes a new Application Programming Interface (API), with an implementation in R, and a companion method called Cloud Pattern API – Process Mining (CPA-PM), for the preprocessing of event logs in a way that addresses many of the challenges identified in the SLR. A case study involving a SaaS company and real event logs related to the trial process of their online service is used to validate the proposed solution.