Tudies that have investigated students’ perceptions of EGAP and ESAP instructions have generally focused on students’ perceived learning of the features of academic discourse that they can transfer to their subject-specific courses. Examining the processes that students go through when trying to adjust to EAP instruction has received little attention. The present study aimed to explore the challenges that Tunisian students faced when trying to adjust to the requirements of an ESAP course to which they had been introduced for the first time. Understanding these challenges can lead to a better understanding of the processes by which students move from the initial learning context to the transfer contexts (Lobato, 2003). The study was conducted over a period of two years and involved two student cohorts. A student cohort of 21 students participated during the academic year 2014-2015 and another cohort of 36 students participated during the academic year 2015-2016. The research consisted of a diary study, in that data were collected solely from the learner diaries that students were asked to keep as part of the learning activities. Results showed that ESAP instruction presented considerable challenges to students during the first semester of the course. These challenges often caused feelings of anger, disappointment, demotivation, and resistance. Despite these challenges, students’ adjustment to the course was clearly observed in the second semester. The findings also revealed that all participants developed a very positive attitude towards the ESAP model at the end of instruction. The findings suggest that ESAP instruction has a greater potential to promote learning transfer because it provides students with a more authentic learning environment. However, the implementation and success of this model in the various Tunisian academic settings depends, on the one hand, on the EAP teachers’ willingness to change their teaching beliefs and practices and, on the other hand, on their preparations to meet the challenges that such a teaching model can pose to teachers.