This paper studies the transactional distance between the students and the tutor as well as the autonomy of students in a postgraduate course of the Hellenic Open University (HOU). The aim of the paper is to examine how the relation between autonomy and transactional distance evolves during an academic year and how this relation is affected by demographic parameters, such as gender, age group and student experience (year of studies). For this purpose an empirical research was conducted and a sample of postgraduate students responded to a questionnaire (which included a scale for transactional distance, a scale for autonomy and demographic questions) during two different time periods within an academic (2012-2013). The results of the statistical analysis showed that during the evolution of the learning process there was a small change in transactional distance, especially for the dimension of co-understanding, while there was also a change in one of the dimensions of autonomy, namely sensitivity to others. However, no relation was observed between transactional distance and autonomy, ether in the first or the second measurement during the academic year. This finding is also regarded in the overall framework of the different critiques and interpretations of Moore's theory.