The British pound and the US dollar have fallen to new low levels against the euro.
The latest falls came after the European Central Bank left interest rates unchanged at 2.5%.
That preserved the interest rate gap between the eurozone and the US, where rates are 1.25%, and that meant the single currency continued to benefit.
Investors are selling dollars and buying euros in order to get a better return for their money.
"It is business as usual now. The euro's bull run continues,"
said analyst Jane Foley at Barclays Capital.
The single currency also continued to strengthen against the pound even though UK interest rates were left on hold at 3.75%.
I believe now that the euro is poised for further gains.
Iain Stannard, BNP Paribas
Gloom about the UK economy is thought to be partly to blame for the pound's fall.
The euro hit a four-year high of $1.1506 on Thursday, just two cents below its level when it was launched on 1 January 1999.
Later on Thursday it fell back to $1.1493.
Against the pound, the single currency hit a record level of 71.87 pence, higher than its level when it was launched.
The rise of the euro, which has also strengthened against the Japanese yen, is worrying companies within the eurozone because it will make their products more expensive abroad.
Interest rate cut
Wim Duisenberg, the ECB's president, insisted the euro's levels were not excessive.
But the single currency's rise is likely to continue, according to Iain Stannard, an economist at BNP Paribas.
"I believe now that the euro is poised for further gains.
"We are likely to see the euro extend the uptrend toward the $1.17 area in the medium term.
Robert Sinche at Citibank said the dollar was under pressure because many traders expected the Federal Reserve to cut its key rate by at least a quarter-point to 1% sometime this year.