It was perhaps the most difficult question either candidate has faced in the tumultuous US presidential campaign so far.
An audience member at the second debate challenged Hillary Clinton and Donald Trump to say one nice thing about each other.
"Regardless of the current rhetoric, would either of you name one positive thing that you respect in one another?" asked Karl Becker.
The crowd - earlier told not to applaud - did anyway.
Ms Clinton went first, praising Mr Trump through a proxy - his kids.
"I respect his children. His children are incredibly able and devoted, and I think that says a lot about Donald," she told the crowd at Washing University in St Louis, Missouri.
"I don't agree with nearly anything else he says or does, but I do respect that. I think that is something that as a mother and grandmother, is very important to me."
Ms Clinton deftly turned her praise for Mr Trump's skills as a father into an argument for why she should be President, moving the debate "off the personal" and onto "what it is I want to do as President".
"I've spent 30 years, actually maybe a little more, working to help kids and families, and I want to take all that experience to the White House and do that every single day."
Mr Trump said he didn't know if Ms Clinton's praise for his children was meant to be a compliment, but he took it as one.
"I'm very proud of my children and they've done a wonderful job and been wonderful kids."
The one thing he respects about Hillary? That despite everything he's thrown at her, she "doesn't quit, she doesn't give up".
"She's a fighter. I disagree with much of what she's fighting for, I disagree with her judgement in many cases, but she does fight hard and she doesn't quit and she doesn't give up, and I consider that to be a very good trait."
The race for the White House has become increasingly heated in recent days, with Mr Trump accusing Ms Clinton's husband - former President Bill Clinton - of raping a woman in the 1970s.
The accusations come in the wake of a recording made in 2005 of Mr Trump saying he liked to grab women "by the p***y", and a TV3 recording from 1993 in which he says it's "fortunate that I don't have to run for political office" because of his views on women.