This paper analyses the problem faced by CEECs wishing to join the Euro who must hit both an inflation and exchange rate criterion during a period of nominal convergence. This process requires either an inflation differential, an appreciating nominal exchange rate, or a combination of the two, which makes it difficult to simultaneously satisfy the exchange rate and inflation criteria. The authorities can use their monetary policy to hit one criterion, but must essentially just hope to satisfy the other one. The paper quantifies the likely size and speed of these convergence effects, their impact on inflation and exchange rates, and their consequences for the simultaneous compliance with both criteria under an inflation targeting setup and under a fixed exchange rate regime. The key result is that under an inflation targeting regime, the nominal appreciation implied by convergence is not big enough to threaten a breach of the exchange rate criterion, but for countries with fixed exchange rates, inflation is likely to exceed the reference value. This result is robust to plausible changes in the assumed convergence scenario.