Effective clinical text processing requires accurate extraction and representation of temporal expressions. Multiple temporal information extraction models were developed but a similar need for extracting temporal expressions in eligibility criteria (e.g., for eligibility determination) remains. We identified the temporal knowledge representation requirements of eligibility criteria by reviewing 100 temporal criteria. We developed EliXR-TIME, a frame-based representation designed to support semantic annotation for temporal expressions in eligibility criteria by reusing applicable classes from well-known clinical temporal knowledge representations. We used EliXR-TIME to analyze a training set of 50 new temporal eligibility criteria. We evaluated EliXR-TIME using an additional random sample of 20 eligibility criteria with temporal expressions that have no overlap with the training data, yielding 92.7% (76 / 82) inter-coder agreement on sentence chunking and 72% (72 / 100) agreement on semantic annotation. We conclude that this knowledge representation can facilitate semantic annotation of the temporal expressions in eligibility criteria.