Autonomy-supportive teachers energize students' agency and initiative. However, few studies consider whether agentically engaged students energize more autonomy-supporting teachers. We asked 2,908 middle and high school students in physical education courses to report their agentic engagement and the autonomy supportiveness of their teachers. Data were collected at four time points over one academic year. We tested two reciprocal effects models relating student perceptions of autonomy-supportive teaching and their agentic engagement: a between-person cross-lag-panel model (CLPM) and a within-person CLPM with random intercept. Both models supported the bidirectional reciprocal relations between perceived autonomy-supportive teaching and agentic engagement. Based on student perceptions, prior agentic engagement led to increased autonomy-supportive teaching and prior autonomy-supportive teaching led to greater agentic engagement. We discuss the practical implications of these findings for classroom research and recommend teachers to inform students early in the school year that they will welcome students' input and initiatives. Educational Impact and Implications Statement: By being more autonomy supportive, teachers can enhance their students' classroom engagement. It is equally true that by being agentically engaged during classroom instruction, students can enhance their teachers' autonomy support. We showed this highly constructive mutual responsiveness between teachers and students in this study. The educational implications are that teachers who want more engaged students can practice greater autonomy-supportive teaching. Similarly, students who want more autonomy-supportive teachers can display greater agentic engagement. For practical reasons, we recommend teachers take the lead to jump-start this reciprocal process with more autonomy-supportive teaching. [ABSTRACT FROM AUTHOR]