Our empirical tests generally support the hypothesis that up to certain values of the average per capita income its growth tends to lead to increased risks of sociopolitical destabilization, and only in the upper range of this indicator its growth tends to be associated with the decrease of sociopolitical destabilization risks. However, our analysis has shown that for various indices of sociopolitical destabilization this curvilinear relationship can be quite different in some important details. On the other hand, we detect the presence of a very important exception. We show that the relationship between per capita GDP and the intensity of coups and coup attempts is not curvilinear; in this case we are rather dealing with a pronounced negative correlation; a particularly strong negative correlation is observed between this index and the logarithm of GDP per capita. We demonstrate that this fact makes the abovementioned bell-shaped relationship with respect to the integral index of sociopolitical destabilization considerably less distinct and makes a very significant contribution to the formation of its asymmetry (when the negative correlation between per capita GDP and sociopolitical destabilization among the richer countries looks much stronger than the positive correlation among poorer countries). However, our analysis shows that for all the other indices of sociopolitical destabilization we do witness the bell-shaped relationship. On the other hand, for example, in relation to such indices, as political strikes, riots and anti-government demonstrations we deal with such an asymmetry that is directly opposite to that mentioned above - with such an asymmetry, when a positive correlation between GDP and instability for poorer countries is much stronger than the negative correlation for richer countries.