A West Midlands Police spokesman said: "This morning two men were arrested under the Terrorism Act in Birmingham.
"The arrests were part of a nationwide counter-terrorism operation co-ordinated by the Metropolitan Police Counter-Terrorist Branch."
The spokesman said no firearms had been involved and the men were still in custody.
June Lethbridge, 85, lives next door to a property on St Margaret's Road, Ward End, Birmingham which was raided by police.
She said a family had lived at the adjacent property for 12 years but she did not know how many were residents and how many were visitors.
She said: "They've always been very pleasant.
"As far as I know, most of the family are in Pakistan for a wedding at the moment. I haven't seen them come back."
Ms Lethbridge pointed out a purpose-built structure in the back garden where she said lessons were held for children.
She said a dozen or so youngsters attended classes, held in English, in the brick built outhouse two or three times a week.
Ikram Ulhaq, whose 12-year-old daughter received lessons in basic Islam from a woman who lived at the address, described the residents as "peaceful people".
He said: "They were teaching Koran and all that to the young kids, how they read the Koran, how they pray five times a day."
Police also continued to search a property in the Alum Rock area of Birmingham on Thursday afternoon.
This was a two-storey shuttered building on Belchers Lane, in the Bordesley Green area of Birmingham, thought to include a business on the ground floor and a residential flat on the first floor.
About 20 officers, including forensic teams were at the scene.
West Midlands Police refused to confirm whether its presence at the address was connected with the anti-terror operation or whether any arrests had been made there.
Local residents said the business had changed hands several times over recent years, going from an industrial cleaning firm to an insurance company and now a company called ACS Management.
Sangita Myska, from the shop, released a statement which said: "We at ACS Management Group had absolutely no involvement in the raids that have taken place at the premises on Aug 10, 2006.
"We are a new company that is renting out the shop unit from the landlord."