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.
Nine thousand images are to be inspected in the case of a Londonderry man charged with committing terrorist offences in the Middle East.