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Rhetorical Role Labeling (RRL) of legal documents is pivotal for various downstream tasks such as summarization, semantic case search and argument mining. Existing approaches often overlook the varying difficulty levels inherent in legal document discourse styles and rhetorical roles. In this work, we propose HiCuLR, a hierarchical curriculum learning framework for RRL. It nests two curricula: Rhetorical Role-level Curriculum (RC) on the outer layer and Document-level Curriculum (DC) on the inner layer. DC categorizes documents based on their difficulty, utilizing metrics like deviation from a standard discourse structure and exposes the model to them in an easy-to-difficult fashion. RC progressively strengthens the model to discern coarse-to-fine-grained distinctions between rhetorical roles. Our experiments on four RRL datasets demonstrate the efficacy of HiCuLR, highlighting the complementary nature of DC and RC.