Counter Terrorism Policing North East have been granted special dispensation to continue question the two Savile Town men arrested on terror charges on Tuesday.
The men were arrested on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism.
Having been detained in a West Yorkshire Police Station since then, a warrant of further detention was issued this morning, enabling police to continue quizzing the suspects.
This morning an extension was approved by the court, giving detectives until April 10 to question the men, aged 52 years and 21 years.
A residential address in Dewsbury remains cordoned off and is still being searched by specialist officers. West Yorkshire Police say that they are continuing to work closely with their partners and communities to reassure local people and protect the public.