The currencies of the Visegrád countries (Poland, the Czech Republic, Hungary,and Slovakia) have been considered by the international financial community as a basket ofcurrencies which are closely related, especially in times of their depreciations. On July 1,2008 the official terminal exchange rate SKK/EUR was fixed. During the following 8months, the remaining three currencies (PLN, CZK, HUF) changed their long-termbehaviour to one of strong parallel depreciation. On the other hand, in the first selectedlong-term period (January 4, 1999 – June 30, 2008), a relatively mixed development ofHUF seemed to exhibit a rather low degree of interdependence with CZK (that had beenappreciating very intensively). The values of the Kendall’s correlation coefficientcalculated for all 3 remaining couples of returns substantially rose in the second period(indicating that similarities between the returns of these exchange rates are stronger in thetimes of crises). We have performed modeling and fitting of the dependencies of the abovementioned couples of returns of currencies in both the mentioned time periods by severalclasses of bivariate copulas, as well as by (optimized) convex combinations of theirelements.