A mule occurs when a coin is produced with mismatched dies. In some countries, the Mints use dies for different denominations with the same dimensions. In these instances, mules have been known to exist and are not that rare.

An example would be a New Zealand/Bahama mule where thousands were struck and they are worth $50 each. The obverse of a Bahama 5 Cent piece was muled with the reverse of a New Zealand 2 Cent piece.

On the other end of the spectrum are the extremely rare mules including a few from the United States. An example would be a mule with a Sacagawea Dollar reverse and a State Quarter obverse.

The photo shown above is a rare example of a Euro 50 Cent reverse that was muled with a Euro 20 Cent reverse. This rare piece is also a "two-tailed" coin because both dies were reverse designs and both are denominations of Euro coinage.