Adaptation and learning over multi-agent networks is a topic of great relevance with important implications. Elaborating on previous works on single-task networks engaged in decision problems, here we consider the multi-task version in the challenging scenario where the state of nature may change arbitrarily. We propose a data diffusion scheme for tracking these changes in real time, and investigate by numerical simulations the corresponding steady-state decision performance. For the slow-adaptation regime, the complete analytical characterization of the agents' status is provided, under the simplifying assumption that the network connection matrix is correctly estimated.