In many distributed learning problems, the heterogeneous loading of computing machines may harm the overall performance of synchronous strategies, as each machine begins its new computations after receiving an aggregated information from a master and any delay in sending local information to the latter may be a bottleneck. In this paper, we propose an effective asynchronous distributed framework for the minimization of a sum of smooth functions, where each machine performs iterations in parallel on its local function and updates a shared parameter asynchronously. In this way, all machines can continuously work even though they do not have the latest version of the shared parameter. We prove the convergence of the consistency of this general distributed asynchronous method for gradient iterations and then show its efficiency on the matrix factorization problem for recommender systems and on binary classification.