Five people, including a 16-year-old boy, have been arrested on suspicion of right-wing terrorism offences.
Officers carried out a series of raids in Keighley, in West Yorkshire, Swindon and Anglesey in Wales.
Following the arrests, bomb disposal experts were called to a property in Keighley after officers discovered potentially suspicious material.
A cordon has been put in place around the property and a number of nearby homes have been evacuated, police said.
Counter Terrorism Policing North East (CTPNE) said two men, aged 29 and 30, and a 28-year-old woman have been arrested in Keighley on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism.
No immediate risk
A 16-year-old boy was arrested in Swindon and a 28-year-old man was arrested in Anglesey on suspicion of the same offence.
All five have been taken to a police station in West Yorkshire for questioning.
A CTPNE spokesperson said the arrests form part of an ongoing investigation into right-wing terrorism.
West Yorkshire Police said two addresses were being searched in Keighley.
A force spokesperson added: Following the discovery of potentially suspicious material at one of the addresses in Keighley the Explosive Ordnance Disposal Unit has been called to provide specialist advice and to arrange the safe removal of the items if required.
As a precautionary measure, a cordon has been put in place and a number of local residents have evacuated whilst examinations are conducted.
We would like to reassure people that these arrests are pre-planned and intelligence-led and there is not believed to be any immediate risk to the local community.