Steady-state detection (SSD) is a critical task in the analysis of dynamic systems, as it enables the reliable evaluation of system behavior by differentiating between stable and unstable states. While SSD techniques have been developed and tested in domains such as signal processing and industrial systems, their application in the information systems domain, particularly in process mining, has been largely overlooked. Specifically, event logs that record the executed behavior of a business process often contain data from both steady and non-steady states, which can distort process mining results, such as performance analysis and remaining time prediction. This paper highlights the importance of SSD in the process mining domain and investigates the applicability of existing SSD solutions. To operationalize this, we propose a two-step framework for detecting steady states in business processes. The framework extracts relevant process characteristics from an event log and applies established SSD techniques to identify periods during which a business process operated in a steady state. We evaluate the framework through experiments that assess its accuracy within a controlled environment using simulated event logs and that demonstrate the benefits of SSD for a downstream process mining task: remaining time prediction. The findings emphasize the potential of SSD for obtaining more accurate process mining insights.