"We will be looking in particular at whether there are benefits."
If found guilty, the companies could face fines of up to 10 per cent of their global turnover, Todd said on Monday.
The commission, the EU's executive arm and chief competition regulator, said in a statement: "The commission will assess the compatibility of each of these airlines' co-operation with European rules on restrictive business practices."
The commission said the probes, for which no deadlines for completion have been set, did not imply it had conclusive proof about any infringement, but that the cases would be given priority treatment.
Brussels said it was investigating whether the agreements reached between the companies meant that they would co-operate more closely than generally accepted, mainly on routes between the EU and North America.
"In particular, the parties to each agreement intend to jointly manage schedules, capacity, pricing and revenue management on transatlantic routes, as well as share revenues and sell tickets on these routes without preference between these carriers," the statement said.
"The commission is assessing whether these joint activities may lead to restrictions of competition on certain transatlantic routes."
The Star Alliance probe covers existing transatlantic co-operation between Lufthansa and United, and between Lufthansa and Air Canada, as well as a proposed four-party agreement between them and Continental, a carrier in the United States.
A spokesman for Lufthansa, the German flag carrier, said the company had been warned of the investigation and that it was co-operating fully.
"It's a normal procedure. We have had constructive exchanges with the European Commission. We are providing the information that it's asking for," he said.
Todd said: "The European Commission doesn't open anti-trust investigations on a routine basis."