Conflict US and European trademark?

Note that the United States uses the "first to use" system, meaning that the first person to use the trademark - in the United States - should be the real owner of the trademark (as opposed to a "first to file" system). Having this said, it is understood in by the United States Patent and Trademarks Office (USPTO) that you start using the trademark once the services are available to the public through a website, therefore if you already have a site online and have had it for some time, then there may be some steps we could take, starting by investigating if the other party has already started using the trademark. A second thing to look for is the classification of the trademark, as Thierry pointed out. We can research these two matters for free in order to find what options we may have.