Large language models (LLMs) reflect societal norms and biases, especially about gender. While societal biases and stereotypes have been extensively researched in various NLP applications, there is a surprising gap for emotion analysis. However, emotion and gender are closely linked in societal discourse. E.g., women are often thought of as more empathetic, while men's anger is more socially accepted. To fill this gap, we present the first comprehensive study of gendered emotion attribution in five state-of-the-art LLMs (open- and closed-source). We (...) investigate whether emotions are gendered, and whether these variations are based on societal stereotypes. We prompt the models to adopt a gendered persona and attribute emotions to an event like 'When I had a serious argument with a dear person'. We then analyze the emotions generated by the models in relation to the gender-event pairs. We find that all models consistently exhibit gendered emotions, influenced by gender stereotypes. These findings are in line with established research in psychology and gender studies. Our study sheds light on the complex societal interplay between language, gender, and emotion. The reproduction of emotion stereotypes in LLMs allows us to use those models to study the topic in detail, but raises questions about the predictive use of those same LLMs for emotion applications. (shrink)