Our empirical tests generally confirm the validity of the Olson-Huntington hypothesis suggesting a bell-shaped relationship between the level of economic development and the level of sociopolitical instability. According to this hypothesis, 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. Thus, for higher values of per capita income we deal with a negative correlation between per capita income and the risk of sociopolitical instability, and for lower values this correlation is positive. As a result, the maximum values of political instability tend to be observed in the mid-range of the GDP per capita spectrum rather than among the poorest or the richest countries. 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 above mentioned 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 assumed by the Olson-Huntington hypothesis. 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. An especially strong asymmetry of this kind is found for such an important index of social and political destabilization, as the intensity of anti-government demonstrations. Thus, we arrive at the following conclusions: (1) Different types of political instability events have different functional relationships to changing levels of GDP/capita. Some do have a curvilinear response, others have a monotonic one. They also are more frequent at certain ranges of GDP/capita that are not the same, but rather are particular to certain types of events. (2) These findings show that certain types of events are more common at lower levels of income and political development, while others are more common at mid-levels, and yet others (anti-government protests, strikes) are more common at higher levels. (3) The functional relationships are most often linear in rising stages, but exponential or logarithmic in their declines. There are thus generally strong asymmetries in how such events react to changes in GDP/cap in the lower vs. upper ranges. (4) The overall notion of a curvilinear relationship between instability and GDP/capita is thus too simple, obscuring important patterns that reveal a trajectory of varying kinds of instability developing and peaking at different levels of economic development.