The paper investigates students’ readiness for autonomy within the context of learning ESP (English for Specific Purposes) at the tertiary level. Developing learner autonomy within the context of higher education is particularly relevant for students in view of pursuing their career goals in the future. The main objective of the study was to find out whether and to what extent students were ready to adopt autonomy within the learning process at the university level. The sample for this study consisted of a total of 79 respondents from Poland (University of Applied Sciences in Tarnow) and Serbia (University of Belgrade, Faculty of Agriculture). A purpose built questionnaire evaluating an aspect of readiness for autonomy was used to probe the participants. In general, students from both subsamples were inclined to place responsibility for their learning on the teacher. Suggestions on how to tackle different autonomy issues and how to broaden the current study are provided in the conclusions.