Djibril Bashir and Valon Avdylim, of Somali and Albanian origin, respectively -- are accused of having fought with the Islamic State (IS) group in Syria.
Avdylim was also charged along with his younger brother Visar with trying to send military equipment to another sibling who was killed in Syria in April 2014.
The trial marks the first time Norway has invoked a new provision under its criminal law allowing prosecution of any "economic or material support to a terrorist organisation," an offence punishable by a maximum of six years in
All three defendants have denied the charges.
The 30-year-old Bashir admitted on Tuesday that he had joined the IS group in 2013., but claimed to have joined in a non-fighting support role.
The prosecution showed images of him and his colleagues posing with weapons, which he then admitted he had carried for self-defence.
Bashir he told the court he was unaware the organisation had been labelled a terror group by the United Nations at the time.
"I noticed that many other insurgents were very corrupt in the way they handled civilians. Many of them set up checkpoints, kidnapped civilians, demanded money and stole," he said of his time in Syria.
"IS were well-organised and disciplined. They helped people with medicines, food, gas and oil, and had increasing popular support."
He claimed not to have witnessed any signs of the brutal violence which has since characterised the organisation.
The two brothers' elder brother Egzon Avdyli, who was for a time spokesman of he extremist Islamic Profetens Ummah group in eastern Norway, was killed last year fighting in Syria.
Norwegian authorities feared that the two main defendants -- who returned to Norway in January last year -- would try to return to Syria or commit an attack on Norwegian soil.
The pair were arrest along with the younger Visar in May. The trial is expected to last for a month.
One of the three accused was recorded by Norway's Police Security Service (PST) boasting that he hated 'infidels' so much that he wanted to attack a kindergarten in Norway, pushing the police to speed up their investigation and arrest them.
"I want to kill everyone, man. From small to large, man. Walk into any nursery, man," the man reportedly said.
Svein Holden, who is defending Valon Avdyli, said that the situation in Syria had changed since his client went to fight.
“It will be a central question what impact it should have that he was in Syria at an earlier time than when this provision came into force,” Holden told Norwegian state broadcaster NRK ahead of the trial. “The situation today is in many ways different from the period when my client was there”.
Fredrik Schøne Brodwall, who is defending a 30-year-old Norwegian Somali, made much the same point.
“My client was in this area in Syria before the provision came into force, so whether it should apply is a question that must be resolved in court,” he said.
According to intelligence services, more than 70 Norwegians have travelled to join jihadist insurgents in Syria and Iraq.