This article addresses distributed estimation problems over asynchronous networks in a set membership framework. The agents in the network asynchronously collect and process measurements, communicate over a possibly time-varying and unbalanced directed graph and may have nonnegligible computation times. Measurements are affected by bounded errors so that they define feasible sets containing the unknown parameters to be estimated. The proposed algorithm requires each agent to compute a weighted average of its estimate and those of its neighbors and to project it onto a local feasible set. By assuming convexity of the measurement sets, the local estimates are shown to converge to a common point belonging to the global feasible set.