Technostress is a phenomenon in which rapid technological advancement affects teachers' psychological well-being. It is an emerging concern in English language education, which may be exacerbated by the advent of generative artificial intelligence (GenAI) tools such as ChatGPT. This study explores the factors that influence technostress among English language teachers using GenAI tools and strategies that can alleviate it. Based on the analysis of qualitative data from semi-structured interviews with 16 instructors at higher education institutions in Hong Kong, the study identifies the rapid advancement of AI technology, inadequate training and lack of experience as contributors to technostress. It also names mitigating strategies including targeted professional development, online engagement and gradual integration. These techniques can foster Technological Pedagogical Content Knowledge (TPACK) and reduce the challenges of incorporating GenAI into English teaching. The findings align with existing literature on the impact of technostress and the role of TPACK. The practical implications include the need for comprehensive training, supportive communities and a balanced approach to AI integration. This investigation also expands the theoretical understanding of technostress in English language teaching and the use of GenAI tools, providing empirical support for existing frameworks. It also suggests directions for future research, which could investigate teacher well-being, effective AI integration and the impact of TPACK.