Based on the TIMSS and PISA results, Indonesian students' mathematics abilities are far below the international average, it’s because students experience difficulties in solving mathematics problems, especially Higher Order Thinking Skills (HOTS) questions. This research aims to determine students' difficulties in solving HOTS questions on two-variable linear equation systems based on the Cooney indicator. According to Cooney, indicators of difficulty are in concepts, principles and verbal. This research uses a qualitative approach and is located at SMP Negeri 1 Turi Lamongan with a sample of class VIIIG students. Subjects were taken using purposive sampling and obtained 1 student with low level, medium level and high level mathematics abilities. This research data was collected through written tests, interviews and documentation. Data analysis method using data condensation, data reduction, data presentation, and drawing conclusions. The results obtained: Students with low mathematical abilities has difficulty using concepts, principles and verbal. Students with moderate mathematical abilities at certain numbers experience difficulty in using concepts, principles and verbal. And students with high mathematical abilities do not experience difficulties in using concepts, principles and verbal. Future research can explore students' difficulties with other types of questions and indicators.