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Inquiry provides opportunities to engage students in authentic science. Although inquiry's underlying principles can motivate students to learn, the challenges that students encounter may hamper their motivation. Thus, the teacher's role in providing motivational support is crucial. This research examines how the interplay among the inquiry's characteristics, the challenges encountered by students, and the motivational support provided by the teacher affects students' expression of motivation throughout an online inquiry process. The messages of both the teacher and the students were examined using self-determination theory (SDT). The results indicate that the students did not automatically embrace the autonomous characteristic of open inquiry. Their expressions of motivation were dynamic, affected by the challenges that they encountered. In contrast, the teacher maintained high levels of autonomy and competence and intertwined these components in a strategy that we term "guided autonomy." The teacher and students expressed high-order expressions of affect. In addition, we found a positive correlation between the teacher's motivational support and the students' expressions of motivation. The results indicate that SDT can provide a powerful framework for understanding students' unfolding motivation throughout a challenging educational process and for guiding teachers' efforts in supporting the motivation of their students in an online environment.