The importance accorded mathematical connections in the professional literature is not properly reflected in the relatively small number of empirical investigations of students' mathematical connections. The purpose of this study was to investigate the mathematical connections that students form and use in solving nonroutine problems. Two main types of mathematical connections are: internal (across mathematical topics) and external (between mathematics and its applications in other fields or in the real world). Tenth-grade students (n=17) were interviewed while solving one of two nonroutine problems, one involving algebra and internal connections, the other involving geometry and external connections. The two problems elicited a wide variety of responses and seemed to require students to operate metacognitively, to recognize the purposes for the mathematical tools they study, and to identify subgoals along the road to a solution, and therefore seem to be a worthwhile means of exploring students' abilities with mathematical connections. (MKR)