KP, ASTM trades in Europe also under Zeller AG or some such name. In ASTM's case it's because they are also trying to sell their products and have them licensed there. Similar to a FDA approval here. You can find them being traded on the 'net and it has no affect on the US stock as far as dilution is concerned etc. You do the EURO conversion and it will be priced to the US equilvalent usually.
You're basically trading the same stock on a different exchange.
I hope that explains what you're asking.
For those who understand no explanation is needed, ...For those who don't none will.