The investigations were launched by the WTO's Dispute Settlement Body (DSB). It was the second time Brussels had made the requests - the first were blocked by the other two states - and under WTO rules they could not be delayed any longer.
The probe into the hormone issue could take six to nine months, but the decision in the tax breaks case could be ready within 90 days, trade officials said.
In the tax row, the EU last month lifted sanctions on $4 billion of US goods after Congress repealed the law - known as the Foreign Sales Corporation (FSC) law.
But it warned that it could reimpose duties on up to 60 percent of the goods from next year if the WTO decided that the US move fell short of what was required.
Brussels is unhappy that, in withdrawing the law, the US Congress will give transitional aid to companies, including Boeing and Microsoft, which benefited from the scheme, and that contracts signed before September 18, 2003, will be exempt.
In the other case, the United States has been applying some $117 million of punitive duties a year on European exports, such Roquefort cheese, mustard, truffles, French hams and soups - and Canada some $9.5 million - in retaliation for the EU's banning of beef imports treated with hormones.
But the EU says that since the WTO first ruled against it in 1988, it has provided scientific evidence in support of its ban, and that Canada and the United States should drop the sanctions or bring a fresh WTO case against it.