Bail eased for Aust terrorist relatives

The father and uncle of an Australian terrorist who are accused of bribing Iraqi officials will now be allowed to travel to certain countries, including Indonesia and Saudi Arabia.

Mamdouh Elomar and Ibrahim Elomar - the father and uncle of Mohamad Elomar - are accused of offering a $1 million bribe to win contracts for their construction company Lifese in Iraq.

The pair, who deny the allegations, had their bail travel conditions eased in Sydney's Court of Criminal Appeal on Tuesday, allowing them to travel to various overseas countries where they have business interests.

Mamdouh's son was the Islamic State terrorist Mohamed Elomar, who gained notoriety after posting a photo of his nine-year-old son holding the severed head of a Syrian fighter.

Mohamed is believed to have died in a drone strike in Syria in June.

After being charged, Mamdouh and Ibrahim failed in April to have their bail conditions eased so they could travel to several countries to pursue business interests.

But on Tuesday - after the commonwealth DPP conceded that the brothers' reasons for travelling abroad were legitimate - the CCA varied their bail conditions to allow this.

They can now to fly to Papua New Guinea, Indonesia, Singapore, Malaysia, Greece, China, Saudi Arabia and the UAE.

Mamdouh is also allowed to visit Lebanon but Ibrahim is not.

The pair has also been ordered to provide $2 million each in security.

The men have previously said they wanted to travel on behalf of their companies - Lifese and Cloudy Bay Sustainable Forestry.

Lifese, the court heard in April, has an average annual turnover of $30 million and Cloudy Bay nets about $5 million per annum.