Boris Johnson and Jeremy Hunt are taking part in the second and final head-to-head debate of the Conservative leadership campaign.
They are facing 90 minutes of questions from Sun newspaper readers.
The event started at 19.00 BST and is being streamed live on the newspaper’s website and broadcast on Talk Radio.
The result of the contest to succeed Theresa May as prime minister will be announced on 23 July, with the winner taking office a day later.
Voting in the postal ballot to choose the next Tory leader began about 10 days ago.
It is estimated that well over half of the 160,000 or so Conservative Party members eligible to take part have already returned their ballot papers.
In Monday’s debate, billed by the newspaper as The Final Showdown, the two men were questioned about their strategies for delivering Brexit, and their policies on domestic issues such as crime, tax and health will also come under scrutiny.
Foreign Secretary Mr Hunt, and his predecessor in the role Mr Johnson, are also being pressed on their foreign policy record, including their relationship with US President Donald Trump.
In the run-up to the debate, the pair have been urged to condemn recent remarks directed at four US Democratic congresswomen by Mr Trump telling them to “go back”.
No 10 has said the comments were “completely unacceptable” while Ruth Davidson, the Scottish Conservative leader, said the two candidates needed to say so publicly.
During a live debate on ITV last week, the two men clashed over Mr Trump’s attacks on the UK’s top diplomat in the US – which led to his subsequent resignation.
After days of criticism, Mr Johnson conceded on Friday that he should have been stronger in his support for Sir Kim Darroch after diplomatic cables in which the diplomat described the White House as clumsy and inept were leaked to a newspaper.
Sky News abandoned plans for a one-on-one TV debate after Mr Johnson declined to take part while the BBC decided not to proceed with a special edition of Question Time featuring the two politicians after Mr Johnson’s team expressed concerns about the format.
The last of 16 UK-wide hustings, in which the two men have faced questions from Conservative Party members, takes place in London on Wednesday.