Federated learning (FL) has been considered as a promising learning framework\nfor future machine learning systems due to its privacy preservation and\ncommunication efficiency. In beyond-5G/6G systems, it is likely to have\nmultiple FL groups with different learning purposes. This scenario leads to a\nquestion: How does a wireless network support multiple FL groups? As an answer,\nwe first propose to use a cell-free massive multiple-input multiple-output\n(MIMO) network to guarantee the stable operation of multiple FL processes by\nletting the iterations of these FL processes be executed together within a\nlarge-scale coherence time. We then develop a novel scheme that asynchronously\nexecutes the iterations of FL processes under multicasting downlink and\nconventional uplink transmission protocols. Finally, we propose a\nsimple/low-complexity resource allocation algorithm which optimally chooses the\npower and computation resources to minimize the execution time of each\niteration of each FL process.\n