A former member of the Defence Forces is seeking to have charges of being a member of so-called Islamic State (IS) and financing terrorism dropped at the Special Criminal Court.
It is expected that they will argue there is not sufficient evidence to convict their client on any of the charges.
The case received widespread attention in 2019 when it emerged that Smith, a former Air Corps soldier who had worked on the Government jet, had been detained in Syria over alleged links to IS.
Smith was arrested at Dublin Airport in 2019 on suspicion of terrorist offences after returning from Turkey in November with her young daughter.
She had travelled to Syria a number of years ago after she converted to Islam.
Smith is charged under Section Six of the Criminal Justice (Terrorist Offences) Act 2005 which makes it an offence to join a foreign unlawful organisation.
It is alleged that between October 28, 2015 and December 1 2019 at a location outside the State, she was a member of a terrorist group styling itself as the Islamic State.
She has also been accused of financing terrorism, by sending 800 euro in assistance by Western Union money transfer to a named individual in 2015.
She has denied the charges.
The trial was scheduled to begin on Tuesday, but the non-jury court will first have to deal with pre-trial application.
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