We tackle the important task of part-of-speech tagging using a neural model in the zero-resource scenario, where we have no access to gold-standard POS training data. We compare this scenario with the low-resource scenario, where we have access to a small amount of gold-standard POS training data. Our experiments focus on Ukrainian as a representative of under-resourced languages. Russian is highly related to Ukrainian, so we exploit gold-standard Russian POS tags. We consider four techniques to perform Ukrainian POS tagging: zero-shot tagging and cross-lingual annotation projection (for the zero-resource scenario), and compare these with self-training and multilingual learning (for the low-resource scenario). We find that cross-lingual annotation projection works particularly well in the zero-resource scenario.