Federated Learning (FL) is a distributed machine learning technique which enables local learning of global machine learning models without the need of exchanging data. The original FL algorithm, Federated Averaging (FedAvg), is extended in this work by means of consensus theory. Differently from standard FL algorithms, the resulting one, named FedLCon, does not need a coordinating server, which represents a single failure point and needs to be trusted by all the clients. Furthermore, the consensus paradigm is also applied to the Adaptive Federated Learning (AdaFed) algorithm, which extends FedAvg with an adaptive model averaging procedure. Performance comparison tests are performed over a real-world COVID-19 detection scenario.