Eamon Bradley, from Benview Estate in Coshquin, was arrested in October 2014, after he returned from Syria.
He is charged with providing training in the making or use of firearms in Syria.
He is also charged with possessing a grenade in Syria with intent to endanger life.
The charges relate to dates between 4 January and 28 October 2014.
Mr Bradley was arrested at his then home in Melmore Gardens in the Creggan area of Derry.
A solicitor told Londonderry Magistrates Court that she was still awaiting the results of investigations being carried out by members of the Police Service of Northern Ireland's E-crime branch.
She said the investigating officer was now in receipt of a number of computer downloads that contain 9,000 images, all of which have to examined forensically.
A four-week adjournment in the case was granted and the defendant was released on continuing bail.

Sir Thomas Winsor was consulted about Avon and Somerset PCC Sue Mountstevens' plans to "call upon" Nick Gargan to resign.
The PCC says Mr Gargan has lost the confidence of the force at all levels, having been found guilty of misconduct.
But some local Conservative MPs say he has been treated unfairly.
In August, Sue Mountstevens became the first police and crime commissioner to say she would start the process of using new powers to call upon a chief constable to quit, a process which would effectively force him out.
She referred her decision to Sir Thomas - her office has not confirmed his response.
But BBC Points West's home affairs correspondent Steve Brodie said he understood the letter backed Ms Mountstevens' decision. Mr Gargan told the BBC he was unable to comment further.
Now the decision will go to the local police and crime panel for scrutiny, although ultimately, Ms Mountstevens has the final word.
Mr Gargan was suspended in May 2014, amid allegations of inappropriate conduct towards female staff.
An IPCC investigation found those allegations were not proven, but that he had "repeatedly breached data protection principles" and had stored "intimate" material on his police-issue phone.
An independent QC-led panel cleared him of gross misconduct, a sackable offence, but found him guilty of eight misconduct charges and recommended eight final written warnings.
But his three predecessors as chief constable said he should quit for the good of the force.
Announcing her decision in August to initiate the process to call upon him to go, Ms Mountstevens said his position had become "untenable".
But MP for Bridgwater Ian Liddell-Grainger said Mr Gargan was the victim of a "witch hunt", and Bristol North West MP Charlotte Leslie said he had been tried in a "media court".

One private hospital told the BBC that 90 people are on a waiting list after it ran out of supplies last week.
Hundreds of thousands of people have signed a national petition for the jab to be offered to all children
It follows a case in England where a mother shared pictures of her daughter dying in hospital from the illness.
Under national guidelines, the vaccine is only available to babies.
All babies in the UK are offered a potentially life-saving vaccine against meningitis B as part of a national immunisation programme.
However, there have been calls for the age limit to be extended to children and teenagers.
Nine thousand images are to be inspected in the case of a Londonderry man charged with committing terrorist offences in the Middle East.
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Moves by a police commissioner to force out her suspended chief constable have been backed by the chief inspector of constabulary, the BBC understands.
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Private hospitals in Northern Ireland are reporting an increase in the number of inquiries from the public about getting the Meningitis B vaccine.