This series of researches made an integrated approach to the theoretical framework of completivity of assetcapital from physical (or manufactured) asset to ecosystems asset（Eco-asset or capital）. The contents include three parts (1) Asset-capital completivity; (2) Definition, composition, classification and comparison of eco-asset; (3) Economic rights and asset-capital completivity. This paper discussed the first part. The author first reviewed the research progresses in the fields of environmental, resources and ecological economics on physical asset, natural asset and eco-asset or capitals, and pointed out that the current hot topic is focused on integration and systemization from produced asset to ecological asset, which have been represented by researches in completion of asset or capital such as conceptual expansion, evaluation methods and mechanisms of property rights. Secondly, the author briefly reviewed the partiality of conceptual category of asset and capital and their incompletivity in the traditional mainstream neoclassical synthesis economics, including conceptual incompletivity, incompletivity of value and incompletivity of rights. The incompletivity of value is the most important issue for current research in this field. Thirdly, the author summarized the conspicuous progresses and some unsolved issues in current researches of asset-capital completion as follows: (1) Connotational expansion: a conceptual system of manmade, natural, human and social capitals has formed; (2) Expansion in forms of property rights: a multiple property system of private, state-owned, common, public, contingent and non-property, [WTBX]etc[WT], has co-existed; (3) Attribute expansion: economically-based attributes have been extended to include biophysical,eco-environmental and socio-cultural attributes for asset or capital; (4) Expansion in scale system for evaluation: a single  scale of value of currency for evaluation has been expanded into a multiple scale system of value, especially, massenergy and spatial scales of value have been included for evaluation; Unsolved key issues include: (1) Conceptual extension of asset or capital needs deep exploration from two levels of humanity and nature; (2) System significance of asset or capital needs be enucleated from a systematical level of structure and function; (3) A combinative mechanism of separability between rights and responsibility for asset or capital; (4) Economic implications of value for interactions among scarcity, efficiency, equity and sustainability in completion of asset or capital  are necessarily thoroughly explored; (5) Research on some important facets of complexity between ecological-economic interactions affecting completion process of asset or capital needs to be re-enforced; Finally, the author pointed out that, establishing a systematic concept of asset or capital is in urgent need for promoting its completing process and then the connotation of this systematic concept were discussed, five rules for asset-capital completion have been presented as systemization, life cycle value, coupling of different categories of value, right-responsibility integration as well as structuralization of value from quantification. 