We study logical properties that concern the preservation of futuredirected obligations that have not been fulfilled yet. Our starting point is a product of temporal and deontic logics. We investigate some modifications of the semantics of the product in order to satisfy preservation properties, without loosing too much of the basic properties of the product. We arrive at a semantics in which we only consider ideal histories that share the same past as the current one, and that enables a characterization of the states in which the obligations propagate. These are the states where any obligation of a formula that concerns the present moment is not violated. When there are such violations, the deontic realm switches to a lower level of ideality.