The prosecution is expected to show a video where the photographer Johan Persson and writer Martin Schibbye received military training, reports SR Ekot.
The two freelance journalists travelled illegally into Ethiopia's restive eastern Ogaden region in the summer. They have pleaded guilty to entering the country without a visa but deny the terror charges.
Thomas Olsson, the journalists' Sweden-based lawyer, spoke with Swedish Radio P1 this morning. "A few of the ministers, including the prime minister, have clearly expressed that they think these journalists are guilty. It creates an uncertainty about how independently the court can act."
He also called Ethiopia's terror law "undemocratic".
Mattias Göransson, who is the editor of domestic news and feature magazine Filter, told the union magazine Journalisten that the two journalists were investigating Lundin Petroleum.
The company has ties to the Swedish foreign minister, Carl Bildt, who previously sat on its board, and has prospected for oil and gas in the disputed region.
Diplomats from Sweden, Germany and the USA are attending the trial.