UPDATED: Police carry out terrorism raids and arrests across Yorkshire today
The men, age 24 and 29, were arrested at separate locations in Huddersfield and Sheffield and searches were being carried out in properties in Huddersfield and Sheffield as well.
They were detained on suspicion of offences under Section 5 of the Terrorism Act.
The operation is based on recently received intelligence and is not connected to the recent terror attack in Manchester, the North Eastern Counter Terrorism Unit has confirmed.
Social media reports said residents living close to both locations reported being startled by large bangs and then seeing scores of police who confirmed the noises were in connection with the method of entry to the properties.
People living around a block of flats between Dun Street and Cornish Street, close to Sheffield's Inner Ring Road, said the bang went off at about 5.30pm this evening.One man who lived in the block said he saw a second-floor flat's door had been blown off.
Others said they saw armed plain-clothed officers in the triangular courtyard in the centre of the modern block.
The flats are fairly new, a short walk from the city centre, in an area which has seen a massive residential redevelopment over the past decade or so.
In the last couple of hours, cordons on the streets surrounding the property were being lifted, although a number of police officers continued to guard the block, which is opposite the Shalesmoor tram stop, as a searches continued.
Similar scenes were reported in Huddersfield, where a large number of armed police were deployed in the Ellison Street area of the town.
A spokesperson added: "The public may have heard loud bangs at the time that police entered the property. We would like to reassurance you that this was part of the method of entry to gain access to the property.
"We understand that people may have concerns as a result of this activity and we are grateful for the patience and understanding of the public while these enquiries are carried out."