In the current debate on the European Union enlargement there is an apparent mythical belief that, if the set of preconditions set by Brussels are fulfilled, rapid and sustained economic growth would ensue, which would allow the newly admitted countries to catch up economically with the better off European countries. An encapsulation of this thesis is the expression: A well functioning competitive market economy, which would be able to withstand competitive pressures inside the EU. Those who accept this thesis are ready to point out to the experiences of Ireland and Spain in Europe, in particular. But the evidence in this regard is not so conclusive. In addition, there is glaring evidence worldwide as to the rarity of catching up. Thence, taking for granted the above hypothesis can be misleading unless the possible sources of growth are examined in a thorough and open-minded way. This paper aims at raising awareness on an issue, which is more complicated to deal with than is conventionally assumed.