The men, aged 32 and 33, have been detained by police in relation to an alleged shooting incident in Glasgow.
Trident Rethink 'Not Required'
The Defence Secretary said "now is not the time to start rethinking'' the UK's nuclear deterrent, on his first visit to the Clyde naval base where it is stationed.
The Trident system was a key issue in the Scottish referendum debate and looks set to play a part in next year's general election.
The deterrent is up for renewal in 2016 and the SNP, which polls suggest could win a majority of Scottish seats, has said it will not lend its support to any party that favours renewal if there is a hung parliament.
Michael Fallon spoke about the issue as he visited Faslane to "affirm his commitment'' to Scotland and the Clyde naval base which will be home to all UK submarines by 2020.
He said: "The decision to renew Trident will need to be taken in 2016 after the next election, but what I can tell you is that every successive government has decided to renew the nuclear deterrent.
"It's kept this country safe since the Second World War and whatever the political complexion, Labour or Conservative, the government has always renewed that deterrent to keep us safe.
"I think we've learned this year that we live in a pretty uncertain world, now is not the time to start rethinking our nuclear deterrent or to get rid of our nuclear submarines.''
The Royal Navy's Trafalgar Class submarines, HMS Talent and HMS Triumph, are being moved to Faslane from Plymouth as the Clyde base becomes the Navy's Submarine Centre of Specialisation.
Mr Fallon met personnel at the base and contractors working to support the fleet of submarines.
He said: "It is so important as we head towards the end of what has been a very important year for Scotland that we continue to affirm our commitment to the country.
"I'm here because this naval base is Scotland's biggest employer and it's growing. It already employs 6,700 and that will go up to 8,200 when it becomes the centre for all the Royal Navy's submarines, and it's increasingly the most important part of Britain's defence.
"The Clyde will be one of the big three naval bases in Britain, Lossiemouth is one of three fast jet airfields and Scotland is also home to one of the brigades, so Scotland is a vital part of Britain's defence - but equally, defence is very important to Scotland in terms of the jobs it brings and particularly here on the Clyde, the high-skilled jobs that it is able to offer.''
The Defence Secretary will also visit BAE Systems in Glasgow today to discuss shipbuilding.
Last month it was confirmed that the UK's new warships will be built on the Clyde after fears the contract could go abroad.
Mr Fallon said there should be ''no confusion'' over where the work on the new generation of Type 26 frigates will be carried out after First Sea Lord Admiral Sir George Zambellas, the head of the Royal Navy, suggested the £4 billion contract for the ships could be awarded outside the UK.
Defence contracts were another key issue in the run-up to September's independence referendum.
Mr Fallon said: "We're already building two carriers in Scotland and three offshore patrols vessels that I announced in August and we're now planning the next generation of combat ships.
"There could be no clearer demonstration of our commitment to Scottish shipbuilding than that.''
Values across the 20 biggest cities are now expected by property analysts Hometrack to increase by 6% to 7% over the course of 2017.
The Coming Home Centre, at the Pearce Institute in Glasgow's Govan area, is one of 20 groups which will expand their vital support and services to thousands of Scots.
Fresh failings have been raised at a criticised police control room over the handling of reports of concern for a vulnerable man who was later found dead.
Most Viewed Pictures On Heart
Recently Played Tracks
To listen live, choose your preferred station:
Now playing: The best feel good music
Deposit £10 to get a £40 Welcome Bonus - That's £50 to play bingo, slots and more!*
Over 50 tracks to make you feel-good. New album out now...
Find your local four day weather report here.
Make Heart the soundtrack to your day and you could be a winner with great prizes up for grabs throughout the day.
Find out more about some of the companies advertising on Heart Scotland- East.