Pirates Mohamed Adeysey and Abdinur Ali are accused of attacking a Japanese-operated tanker in the Arabian Sea in March 2011 and threatening the ship's captain and 23 crewmembers, The Yomiuri Shimbun reported Wednesday.
The two defendants, along with two others believed to be juveniles, were apprehended by the U.S. Navy the following day and extradited to Japan a week later.
Japan's Antipiracy Law, passed by the Diet in 2009, covers acts of piracy against vessels in territorial waters or on the high seas regardless of whether they are Japanese or foreign-registered.
The maximum penalty upon conviction is life in prison.
At Tuesday's hearing, defense lawyers called for charges against their clients to be dropped but did not elaborate on their claim that the Antipiracy Law is unconstitutional.
A senior prosecutor said he is concerned whether the trial will proceed smoothly.
"We can't predict what the defendants will say," he said.
One major issue is that the two defendants have to rely on translations from Somali to English and then from English to Japanese, or vice versa, in order to communicate.