Problem solving is considered an essential ability for becoming an expert in physics, and individualized feedback on the structure of problem-solving processes is a key component to support students in developing this ability. Problem-solving processes consist of multiple elements whose order forms the sequential structure of these processes. Specific sequential structures can be expected to better reflect expert problem solving and more likely lead to successful solutions. However, this sequential structure often receives limited attention in assessments, thereby neglecting possibly valuable diagnostic information that could be used for individualized feedback. Consequently, a deeper understanding of the sequential structure of students' written physics problem-solving approaches could leverage novel potentials for physics instruction and feedback provision. This study therefore aimed to examine how the sequential structure of written problem-solving approaches differs between high- and low-performing problem solvers as well as to what extent specific sequential elements are predictive of problem-solving performance. To achieve this, we employed methods from process mining and sequence analysis research. Our findings revealed that low-performing problem solvers often lack structure in their problem-solving approaches, contrasting with notably more systematic approaches of the high-performing problem solvers. Additionally, the order in which assumptions and conceptual aspects are addressed in a problem-solving approach seems to be an indicator of problem-solving performance. The findings of this study enhance our understanding of physics problem-solving processes and highlight opportunities for improving instruction and feedback for physics problem solving by considering the sequential structure of students' physics problem-solving approaches.