The research study examines the use of cohesive devices in the argumentative essays of Polish undergraduates, using both quantitative and qualitative analysis. Thirty-two essays were collected from three higher institutions from Poland. The analysis is based on the Halliday and Hasan (1976) framework on cohesion in texts. Firstly, the analysis is conducted by estimating the average frequency of cohesive ties in all essays, their distance, and the distribution of cohesive chains. This examination indicates that students used a variety of cohesive ties and chains. The most frequent tie used was lexical cohesion, followed by reference and conjunction ties. The problems with the use of cohesive devices are also under investigation as Polish students had some difficulties in employing cohesive ties appropriately or effectively. The analysis also includes the comparative study of essays as regards the use of cohesive devices in two proficiency levels, and in relation to writing quality. This examination did not provide conclusive results; however, some interesting findings were reported.