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Domain Adaptation methodologies have shown to effectively generalize from a labeled source domain to a label scarce target domain. Previous research has either focused on unlabeled domain adaptation without any target supervision or semi-supervised domain adaptation with few labeled target examples per class. On the other hand Positive-Unlabeled (PU-) Learning has attracted increasing interest in the weakly supervised learning literature since in quite some real world applications positive labels are much easier to obtain than negative ones. In this work we are the first to introduce the challenge of Positive-Unlabeled Domain Adaptation where we aim to generalise from a fully labeled source domain to a target domain where only positive and unlabeled data is available. We present a novel two-step learning approach to this problem by firstly identifying reliable positive and negative pseudo-labels in the target domain guided by source domain labels and a positive-unlabeled risk estimator. This enables us to use a standard classifier on the target domain in a second step. We validate our approach by running experiments on benchmark datasets for visual object recognition. Furthermore we propose real world examples for our setting and validate our superior performance on parking occupancy data.