In this paper, we introduce a novel on-line Distributed Expectation-Maximization (DEM) algorithm for latent data models including Gaussian Mixtures as a special case. We consider a network of agents whose mission is to estimate a parameter from the time series locally observed by the agents. Our estimator works online and asynchronously: it starts processing data as they arrive with no need of a reference clock, common to all the agents. Agents update some local summary statistics using recent data (E-step), then share these statistics with theirs neighbors in order to eventually reach a consensus (gossip step), and finally use them to generate individual estimates of the unknown parameter (M-step). Our algorithm is shown to converge under mild conditions on the gossip protocol, freeing the network from feedback communications; hence making this DEM algorithm particularly well suited to Wireless Sensor Networks (WSN).