Marylebone magistrates in London granted an order allowing Michael Smith, an engineer, and his wife, Pamela, to be held without charge at Paddington Green top security police station.
It is understood Mr and Mrs Smith, from Kingston upon Thames, south-west London, are being questioned by Special Branch officers investigating allegations relating to military aerospace secrets.
Scotland Yard last night refused to confirm the identity of the couple or to say whether they were being held under Section 1 or Section 2 of the Act.
Section 1 covers espionage and serious security charges. Section 2 deals with more technical breaches of the Act and carries lesser penalties.
British Aerospace yesterday rejected newspaper reports that Mr Smith had ever worked for it or any of its contracting companies.
'He lives in Kingston, we have a major site in Kingston, and so people have assumed he has something to do with us,' a spokeswoman said. 'But he hasn't'
Some reports said Mr Smith was employed by a company that has contracts with BAe's military aircraft division.
One BAe official said he used to work for GEC Marconi, one of Britain's largest defence electronics firms.
Mr and Mrs Smith were arrested at their home on Saturday and taken away separately for questioning. Applications for their continued detention were also held separately. It is understood a number of documents taken from their home are being examined by police.