During the last two decades, universities around the world have increased the adoption of English-medium instruction (EMI) as a way to enhance internationalisation and global competitiveness. EMI adoption presents a wide range of opportunities, but it also presents some challenges, being one of them the potential impact on students' academic performance. This paper analyses the impact of EMI on the academic performance of the students in a Spanish university. The objective is to extend previous research, that shows contradictory conclusions. In the first part of the paper, using a multiple linear regression model to control key covariates, we have compared the performance of 229 EMI vs 635 Non-EMI students, corresponding to cohorts 2013-2014 to 2017-2018, considering the average grade in the 10 subjects of the first course. In the second part, we focus on the 2017-2018 cohort (49 EMI vs 116 Non-EMI students), carrying out a longitudinal study of its behaviour during two academic years in four different subjects. The results show that there are no statistically significant differences in academic performance between EMI and non-EMI students, ie language of instruction does not play a relevant role in academic performance.