Robustness to non-stationary conditions is essential to develop stable and accurate wearable neural interfaces. We propose a novel adaptive electromyography (EMG) decomposition algorithm that builds on blind source separation methods by leveraging the Kullback-Liebler divergence and kurtosis of the signals as metrics for online learning. The proposed approach provides a theoretical framework to tune the adaptation hyperparameters and compensate for non-stationarities in the mixing matrix, such as due to dynamic contractions, and to identify the underlying motor neuron (MN) discharges. The adaptation is performed in real-time (~22 ms of computational time per 100-ms batches). The proposed adaptation algorithm significantly improved all decomposition performance metrics with respect to the absence of adaptation in a wide range of motion of the wrist (80°). The rate of agreement, sensitivity, and precision were ≥ 90% in ≥ 80% of the cases in both simulated and experimentally recorded data, according to a two- source validation approach. The findings demonstrate the feasibility of accurately decoding MN discharges in real-time during dynamic contractions from wearable systems mounted at the wrist and forearm. Moreover, the study proposes an experimental validation method for EMG decomposition in dynamic tasks.