Fully concurrent models of distributed object systems are specified using linear temporal logic that does not per se cope with concurrency. This is achieved by employing the principle of local sequentiality: we specify from local viewpoints assuming that there is no intra-object concurrency but full inter-object concurrency. Local formulae are labelled by identity terms. For interaction, objects may refer to actions of other objects, e.g., calling them to happen synchronously. A locality predicate allows for making local statements about other objects.