Context: Manual qualitative data analysis is time-intensive and can compromise validity and replicability, affecting analysis design, implementation, and reporting. Large Language Models (LLMs) enable human-bot collaboration in Software Engineering (SE), but their potential for qualitative data analysis in SE remains largely unexplored. Objective: The objective of this study is to design and develop an LLM-based multi-agent system that synergizes human decision support with AI to automate various qualitative data analysis approaches. Methods: We used LLM-based multi-agents systems to assist the qualitative data analysis process, deploying 27 agents, each responsible for a specific task, such as text summarization, initial code generation, and extracting themes and patterns. Results: The main findings are: (1) the LLM-based multi-agent system accelerates the qualitative data analysis process, (2) the system effectively automates tasks such as text summarization, initial code generation, and theme extraction, and (3) the publicly accessible code facilitates validation and further evaluation. Conclusion: The proposed LLM-based multi-agent system automates qualitative data analysis process, creating opportunities for researchers and practitioners. Future improvements focus on enhancing multilingual performance and integrating continuous expert feedback. The source code of proposed system and system details can be found here: https://github.com/GPT-Laboratory/Qualitative-Analysis-with-an-LLM-Based-Agentts
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