The aim of this paper is to detect periods in which two currencies can be classified as being the'same' asset. Two currencies can be treated as the same asset if their exchange rates vis-à-vis the same base currency are cointegrated with a cointegration vector that is consistent with the triangular arbitrage condition. In a first step, it is theoretically derived under which conditions,with respect to the process of the fundamentals, the exchange rates are cointegrated. The empirical results yield that periods of strong comovements of the US dollar and Pound sterling based upon the Euro prevail during the 1990s and periods of comovements of Euro and Pound sterling denominated in US dollar prevail since the introduction of the Euro. Furthermore, no long-run relationships canbe discovered. This paper gives four major innovations to the literature. It first shows under which conditions exchange rates can be bivariately cointegrated. Secondly, it uses the cross-rate identity to test forcointegration, i.e. deducing recursively. Thirdly, it applies the cointegration methodology within atriangular framework by detecting cointegration between exchange rates that are not only denominated in U.S. dollars. And lastly, it shows that comovements between two exchange rates exist ina narrower sense but only in short periods, whereas the economic variables which have caused therelationship are explored.