Computer simulations create a context that is well fitted for exploratory or discovery learning. The aim of the present two studies was to gain deeper insight into what constitutes exploratory learning and to assess the effects of a number of instructional support measures. The domain involved was control theory at the university level. In the first study we made an inventory of exploratory learning processes by observing 17 students working with a computer simulation and analyzing students' thinking-aloud protocols. Subjects received a structured assignment with hints as an instructional support measure. In the second study, 91 students received an open-ended assignment with instructional support that consisted of an information sheet and a set of fill-in forms. On both sheets and forms, six cells were presented. A cell was given for each of the following six learning processes: identifying variables and parameters, generating hypotheses, designing an experiment, predicting, interpreting data, and drawing of conclusions. Information sheets were either of a domain specific or of a general nature. The set of fill-in forms were either free or had the cell HYPOTHESIS already filled in. The statements of the students on the fill-in forms were analyzed in a stepwise order. Twenty-two detailed learning processes were identified and classified. Two of the main classes of processes are transformative and regulative. Both studies showed that students were reluctant to apply learning processes that are considered characteristic for exploratory learning. Furthermore, students had problems with the exploratory learning processes, especially with the processes of generating hypotheses, interpreting data, and drawing conclusions. Effects of the instructional support measures were not conclusive. Hints did not result in significant improvements of the study process. Supporting learning processes with information sheets appeared to help students in performing learning processes, but no different effects of domain specific and general information could be found. Students who were provided with hypotheses showed a higher global activity level and higher scores in domain correctness of their learning processes.