Theoretical and methodological positions and experience of applying ASPID - and APIS - methodologies in the estimation of emergent properties of water objects are considered. Axiology, axiometry, methods, model-classification of integral assessment of trophic status, water quality, stability of water bodies and streams, ecological well-being of water objects have been developed. The questions of construction of multilevel and multi-criteria models-classifications of emergent properties (trophic status, stability, well - being), stages and results of evaluation studies are considered. Representations of the ecological status (ES) are formed on the basis of a study of the ability of the aquatic ecosystem to produce organic matter, assess water quality from the position of biocentrism or anthropocentrism (or combination of approaches) and the stability of the water body to change the parameters of natural and anthropogenic regimes. The idea of the ecological well - being (EB) of a water body is formed on the basis of an axiological approach from the standpoint of biocentrism or anthropocentrism or a combination of approaches. The criteria and evaluation scales that form the basis of the integral estimation are proposed. Approaches to the calculation of priorities (weights) for the convolution of indicators for different convolution levels have been developed. These approaches take into account the priorities in the assessment from the standpoint of "aquatic ecology" (biocentrism) or "hydroecology" (anthropocentrism). Axiology, geoecological analysis and geosituational approach allow to unite all approaches. Author's definitions of the main terms are discussed. Examples of selection of representative criteria, stages and results of evaluation studies are given. The construction of integral indicators of trophicity is examined using the example of marine and inland water bodies of the Arctic zone of Russia (APR) and the North-West of the Russian Federation. The mechanisms of the formation of stability for water bodies and watercourses are considered, which determine the consideration of two main types of stability: 1-adaptation (reservoirs) and 2-regeneration (watercourses). The construction of integrated indicators of sustainability is examined using the example of water objects in the North and North-West of the Russian Federation. Axiology and axiometry, models of integral estimation of ES and EB of reservoirs on the example of small lakes of the northwestern Ladoga lakes, lakes of the Northwest of the Russian Federation are considered. The models of the integral estimation of the EH of the watercourse-catchment system and the results of an integrated assessment of EH for hypothetical areas and real key geosystems from the standpoint of biocentrism and anthropocentrism are considered.