A 16-year-old boy from Swindon is among five people arrested by Counter Terrorism Policing North East on suspicion of terror offences.
The other four people arrested include two men and one woman from Keighley in West Yorkshire between the ages of 28 and 30, and a 28-year-old man from Anglesey in North Wales.
All five were arrested on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism under section 41 of the Terrorism Act 2000.
They have been taken to a police station in West Yorkshire for questioning.
A number of properties are being searched in connection with the arrests.
The arrests form part of an ongoing investigation led by Counter Terrorism Policing North East into to Right Wing Terrorism.
Wiltshire Police said in a statement: "We recognise that local people may have concerns as a result of this activity. We would like to reassure them that these arrests are pre-planned and intelligence led and there is not believed to be any immediate risk to the local community.
"We are grateful for the understanding, patience and support of local residents while these enquiries continue."