The trial of Syrian nationals Muwafaka Alabash and Asem Alfrhad opened at the criminal court in the western Turkish resort of Bodrum, the Dogan news agency reported. If convicted, they face up to 35 years in jail.
They are accused of smuggling migrants and causing the deaths of five people, including three-year-old Aylan Kurdi, his five-year-old elder brother Galip and his mother Rihan.
The victims were among some one million people who last year sought to cross the Aegean Sea from Turkey in a bid to reach EU member Greece.
The photograph of Aylan Kurdi, in his toddler's clothes and face down in the sand, washed up on a Turkish beach, shocked public opinion in Europe and to a certain extent prompted greater action from EU leaders in the migrant crisis.
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Dogan reported that Aylan Kurdi's father, Abdullah Kurdi, who survived the sinking of the boat, is also on trial in absentia over his role in the disaster. It was not immediately clear what charges he faces.
Dogan confirmed he was not in court but the two Syrian suspects, who are currently in custody, were brought to the court by the police.
Turkey has become the major hub for Syrian, Afghan, Iraqi, Eritrean and other refugees and migrants seeking to undertake the risky crossing to the European Union in a flow that has caused huge alarm across the continent.
The Turkish government struck a deal with the EU in November to halt the flow of refugees, in return for three billion euros (USD 3.2 billion) in financial assistance.