This paper presents results of a longitudinal study in the transition to independent graduate studies in mathematics. The analysis of the data collected from 24 students doing a PhD in mathematics revealed the existence of three transitional stages within the PhD degree, namely "Adjustment", "Expertise" and "Articulation". The focus is on the first two transitional stages, since the data collection focused mainly on these. Based on the first two transitional stages and the students' ways of dealing with them, which were called "survival strategies", three types of students were identified. The importance of motivation for each transitional stage and the successful transition overall are considered as well.