Three people were arrested under the Terrorism Act after police found "suspicious material" at two homes, officers have confirmed.
The Leeds-based Counter Terrorism Unit said the arrests followed searches at two residential properties in the Rotherham area of South Yorkshire at the weekend.
A spokeswoman said two men aged 34 and 37, and a woman aged 20, were initially arrested on suspicion of burglary and drugs offences. They remain in custody.
It is understood the arrests are not related to Islamic extremism.
The spokeswoman said the three people had been arrested on suspicion of offences under the Terrorism Act 2000.
She said suspicious material was discovered at a house in Aston, near Rotherham, during the early hours of Sunday as officers conducted routine inquiries into a reported burglary.
She added: "Subsequent inquiries led to a second address in Swallownest and the arrests under the Terrorism Act. All three suspects have been detained in South Yorkshire for questioning."
A judge granted a custody extension on Monday.
The spokeswoman said: "A number of precautionary safety measures have been taken including the support of specialist teams who have carried out thorough searches at both addresses, recovering further items from the second address. Neither property is believed to present a risk to local residents and, indeed, other than for a short period, the adjacent addresses have remained occupied throughout.
"Inquiries are now under way by officers from the Counter Terrorism Unit-Leeds and South Yorkshire Police. Searches at one premise are now concluded but they continue at the other address."
