Five men have been arrested under terrorism laws in two separate operations, police have confirmed.
Dawn raids took place at four addresses in Manchester
Police arrested two men, aged 25 and 29, in Halifax, West Yorkshire.
Another two men, both 24, were arrested in Cheetham Hill, Manchester, and a fifth man, 32, was held after his arrest in that city's Longsight area.
It is thought the Manchester operation is linked to an incident earlier this month in which a terror suspect absconded, breaching a control order.
The BBC's Home Affairs correspondent Danny Shaw said the British-born man, in his 20s, disappeared while under an order which imposes a type of house arrest on terror suspects.
He is thought to have gone abroad and is not believed to be one of the three arrested in Manchester, Mr Shaw says.
Greater Manchester Police said the operation was carried out at four addresses and three were still being searched.
Officers have liaised with representatives of the local community and produced leaflets giving information about the operation.
Police raided addresses in Halifax at about 6am
A police spokeswoman said: "At this stage, there is no intelligence of any planned terrorist activity in the UK and the arrests are part of an ongoing investigation."
Meanwhile, two men are being taken to a London police station following the unrelated raids in Halifax.
The pair were arrested in connection with a search for extremist material which may have been used to radicalise individuals or promote ideologies supporting terrorism, according to Mr Shaw.
A Scotland Yard spokeswoman said: "At approx 6am today in an intelligence-led operation, two men were arrested in West Yorkshire under the Terrorism Act 2000."
The arrests were made by officers from the Metropolitan Police's Counter Terrorism Command and the West Yorkshire Police.
Police are now searching four addresses in the Halifax area, one of which is thought to be in the Pellon area.
The Manchester raids are not connected to those in Halifax
A flat in north London is also being searched as part of the same operation.
A spokesman for the West Yorkshire force said high-visibility police will patrol affected areas to provide reassurance.
A meeting has taken place between police and community leaders at the Queens Road Neighbourhood Centre in Calderdale.
It is one of a number of venues which will open throughout the day to provide local people with information about the day's events.
Police stressed there were no links with the arrests made in Manchester.