Development convergence of countries implies the attitude according to which economies with low GDP per capita have marked economic growth rate only if they are under the point that represents long term economic balance, which is usually the case. This was at the same time one of the key messages of neoclassical growth model by the Nobel Laureate for economics Robert Solow in 1985. However, numerous researches show that there is no clear pattern of convergence of countries at the different development level. Empirics confirms that a number of initially underdeveloped economies have had high growth rates, while a great number of countries have revealed low growth rate in the long run. So, for a number of countries the hypothesis on development convergence has been proved right. In contrast, for the majority of countries, empirical research have not proved the tendencies that developing countries according to the criterion of the height of GDP per capita in time have legally come closer to economically developed countries. In short, the convergence of countries with different initial levels of economic development could be a reasonable hypothesis for some lesser-developed countries in a certain period of time, but that is not the case of most developing countries.