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Federated learning (FL) enables collaborative model training without centralizing data. However, the traditional FL framework is cloud-based and suffers from high communication latency. On the other hand, the edge-based FL framework that relies on an edge server co-located with mobile base station for model aggregation has low communication latency but suffers from degraded model accuracy due to the limited coverage of edge server. In light of high accuracy but high-latency cloud-based FL and low-latency but low-accuracy edge-based FL, this paper proposes a new FL framework based on cooperative mobile edge networking called cooperative federated edge learning (CFEL) to enable both high-accuracy and low-latency distributed intelligence at mobile edge networks. Considering the unique two-tier network architecture of CFEL, a novel federated optimization method dubbed cooperative edge-based federated averaging (CE-FedAvg) is further developed, wherein each edge server both coordinates collaborative model training among the devices within its own coverage and cooperates with other edge servers to learn a shared global model through decentralized consensus. Experimental results based on benchmark datasets show that CFEL can largely reduce the training time to achieve a target model accuracy compared with prior FL frameworks.