The paper presents empirical results on an import prices equation to the case of the small open Hellenic economy, during her course to the European Monetary Union, in the 1980s until mid-1990s. The analysis employs cointegration theory to examine the long-run co-movements of prices, effective exchange rate of GRD and unit labour cost of the European countries, which export to Greece. Innovation accounting is also used so as to detect the dynamics of the data set. We found slight evidence to support long run equilibrium, however, it was only the Hellenic inflation rate, which was adjusting to the deviations from this. The fragile stability of the system is confirmed by the impulse response functions examination where the exchange rate of the GRD do not converge to its long-run values, even after a 3 years period from the one unit-shock in various innovations. The determinant role of the growth rate of the unit labour cost and therefore of European countries’ prices to the exchange rate of GRD, to the Hellenic inflation rate, and less to the growth rate of the import prices is (1) justified by its high proportion to their variance decomposition and (2) became apparent approximately after 9 months. The latter seems to amount to the “contract-period” in the Magee’s terminology.