It is substantiated that an important condition of local budget management system functioning and improvement is the budget financial condition full and comprehensive analysis, which should be conducted on the basis of financial stability indicators. Based on the research of domestic and foreign scholars, the author systematized and deepened the theoretical basis of "financial stability of local budgets" concept, the characteristics of which are defined in the following aspects: 1) the ability to stably ensure budget solvency and balance at the expense of internal financial resources; 2) the ability to independently and on a permanent basis to ensure the territory socio-economic development regardless of transfers from the central government; 3) the ability to timely and fully involve local authorities in their own funds to perform their functions and provide the population with a high level of public goods. It is proposed to understand the budget financial stability in two ways: on the one hand, as a system of administrative-territorial units’ financial condition indicators, and on the other - as a tool for local budgets financial resources effective management. The main components of financial sustainability of local budgets are identified and grouped, in particular: solvency, balance, independence, financial ability, efficiency and effectiveness, debt security, intergenerational justice. The classification features of the budgets financial stability are systematized and expanded. The importance of determining the budget financial sustainability type is substantiated, as it allows: to use the method of benchmarking; to identify similar problems in the budget process and the budgetary mechanism inherent in the budgets of certain type sustainability; to develop an effective financial strategy. The paper identifies that in the process of assessing the local budget financial stability is important to analyse in detail the financial condition of the local budget and identify the main problems in the budget process. The results of analysis are the information basis for the formation of measures to improve the filling of the local budgets revenue side and eliminate shortcomings in the implementation. The paper substantiates the methodological approach to assessing the local budgets financial stability in Ukraine, which is based on the indicators system and allows to assess the balance, financial independence, efficiency, effectiveness, debt burden. It was found that the local budgets financial stability indicators system is not unified for all types of budget and may change depending on the objectives and completeness of information. In any case, it is important to take into account the population, population density and other indicators that are specific to a particular administrative-territorial entity and require appropriate adjustment of regulations. Based on the analysis, the upward dynamics of the local budgets of Ukraine financial condition for the study period was stated. It is shown that it was a consequence of the decentralization reform positive impact on the formation and use of local budgets financial resources. The trend towards increasing the local budgets financial stability, despite the economic crisis, is noted. The expediency and possibility of using the neural networks method in the budgets financial stability assessment process, in particular Kohonen's self-organization maps, are substantiated. Its advantages in determining the local budgets financial sustainability in comparison with other research methods, in particular integrated and matrix have been shown: simplification of assessment due to its implementation speed and automaticity; ability to evaluate a large number of objects and parameters; reduction of research subjectivity; clear visualization, lack of input data normalization and others. It is determined that it is important in domestic practice to ensure the financial stability of local budgets over time, which should become an integral part of territories budget policy. As a result of the research the theoretical bases of budgetary policy strategy formation on maintenance of the local budgets financial stability by definition of the basic stages of its development and realization by local executive bodies and/or local self-government bodies have been improved.
