The Global Financial Crisis caused by the collapse of the U.S. financial system had immense repercussions for the Eurozone countries. The fall-out of the global crisis turned out to be quite different for the “economically healthy” economies of Northern Europe and “core” and the economies of the Southern “sick periphery”, with the latter still suffering and trying to recover. The problem was acknowledged to be the difference of international competitiveness between the countries of these two groups, while its increase was considered to be substantial for the recovery of those countries which were most forcefully hit from the crisis. Countries of the periphery tried to improve their price/cost competitiveness by implementing internal devaluation and fiscal consolidation policies expecting an improvement on their international competitiveness and balance of payments performance. However, the adopted policies did not bring about the anticipated recovery and extended the period of turbulence for the Member States of the Eurozone and especially for those in South Europe like Greece. The negative experience of Greece and other countries of the periphery confirmed the perceptions of those economists who argued that a country could enhance its international competitiveness in a meaningful and lasting way only through the development of its non-price/technological competencies and structural strengthening of its technological capabilities and national innovation system. Thus, this research investigates how the international competitiveness of Eurozone Member States is affected on the one hand, by its international cost/price competitiveness, and on the other hand by its technological competencies. The econometric findings of this research lead to the recommendation of a policy orientation focusing on the case of Greece.