Key to fast adaptation of language technologies for any language hinges on the availability of fundamental tools and resources such as monolingual/parallel corpora, annotated corpora, part-of-speech (POS) taggers, parsers and so on. The languages which lack those fundamental resources are often referred as under-resourced\nlanguages.\n\nIn this thesis, we address the problem of cross-lingual dependency parsing of under-resourced languages. We apply three methodologies to induce dependency structures: (i) projecting dependencies from a resource-rich language to under-resourced languages via parallel corpus word alignment links (ii) parsing under-\nresourced languages using parsers whose models are trained on treebanks of other\nlanguages, and do not look at actual word forms, but only on POS categories. Here\nwe address the problem of incompatibilities in annotation styles between source side parsers and target side evaluation treebanks by harmonizing annotations to a common standard; and finally (iii) we add a new under-resourced scenario in which we use machine translated parallel corpora instead of human translated corpora for\nprojecting dependencies to under-resourced languages.\n\nWe apply the aforementioned methodologies to five Indian languages (ILs): Hindi, Urdu, Telugu, Bengali and Tamil (in the order of high to low availability of treebank data). To make the evaluation possible for Tamil, we develop a depen\ndency treebank resource for Tamil from scratch and we use the created data in\nevaluation and as a source in parsing other ILs. Finally, we list out strategies that\ncan be used to obtain dependency structures for target languages under different\nresource-poor scenarios.