Despite the prevalence of undergraduate drop-in mathematics tutoring, little is known about the behaviors of this specific group of tutors. This study serves as a starting place for identifying their behaviors by addressing the research question: what observable behaviors do undergraduate drop-in mathematics tutors exhibit as they interact with students? We analyzed 31 transcripts of tutoring sessions using inductive coding, finding 83 observable behaviors. We discovered that tutors used behaviors aimed at engaging students, while primarily retaining control of the decision making and problem-solving process. Although tutors asked students to contribute to the mathematics, they often asked a less demanding question before the student had a chance to respond to the initial question. Our findings reveal the existence of opportunities for student learning in tutoring sessions as well as potential areas of growth for tutors. We present questions for future research that arose from analysis of the data and discuss how our results may be used in tutor training.