Abstract. The problem of delay of growth rates of the world economy is very significant in modern conditions. The chronic stagnation of the countries with developed economy and the systematic economic problems in developing countries are the key causes of the given situation. The investigation of the tendencies, problems and prospects of the development of the world economy is carried out in the work. In particular, the analysis of the current tendencies concerning change of GDP of the leading countries during 2019-2020 is made. It showed that the USA and China remain world leaders in rates of economic development considering volumes of their GDP. The definition of the perspective GDP volumes of the world leading countries for the future is carried out. It gave an opportunity to see that their perspective volumes of GDP will slowly increase during the next 5 years. The identification of the reasons of delay of development of the world economy is carried out. It showed that it is caused by the following factors: the delay of growth in the countries with emerging market; economic problems in China and the reduction of prices of exchange goods and gradual toughening of monetary and credit conditions in the USA. The way of activization of development of the world economy is defined. It is presented in the form of technique, which provides that developers of state policy around the world will concentrate their attention on investments into the most important branches of economy. In general, the results of the research are based on forecasting of perspective volumes of GDP of the leading world countries that, in turn, allows recommendations formulating for development of the state external economic policy for the purpose of activization of their economic development at the world level. Keywords: world economy, development, GDP, tendencies, problems, prospects, forecast.