Multi-Source-Free Unsupervised Domain Adaptation (MSFUDA) requires aggregating knowledge from multiple source models and adapting it to the target domain. Two challenges remain: 1) suboptimal coarse-grained (domain-level) aggregation of multiple source models, and 2) risky semantics propagation based on local structures. In this paper, we propose an evidential learning method for MSFUDA, where we formulate two uncertainties, i.e. Evidential Prediction Uncertainty (EPU) and Evidential Adjacency-Consistent Uncertainty (EAU), respectively for addressing the two challenges. The former, EPU, captures the uncertainty of a sample fitted to a source model, which can suggest the preferences of target samples for different source models. Based on this, we develop an EPU-Based Multi-Source Aggregation module to achieve fine-grained, instance-level source knowledge aggregation. The latter, EAU, provides a robust measure of consistency among adjacent samples in the target domain. Utilizing this, we develop an EAU-Guided Local Structure Mining module to ensure the trustworthy propagation of semantics. The two modules are integrated into the Evidential Aggregation and Adaptation Framework (EAAF), and we demonstrated that this framework achieves state-of-the-art performances on three MSFUDA benchmarks. Code is available at https://github.com/SPIresearch/EAAF.