The billionaire was the star of the show during the event - but faced questions about his remarks on women and Mexican immigrants.
Donald Trump stole the show during the first Republican presidential debate in Ohio - with rapturous applause and booing from the audience along the way.
The outspoken billionaire, who has stormed to the top of many nationwide opinion polls recently, refused to pledge that he would throw his support to the person who secures the Republican Party's nomination.
He also suggested that he may run as an independent if he isn't chosen - which could split the vote and help the Democrats regain the Oval Office in 2016.
However, Trump said: "I want to win as a Republican, I want to run as a Republican nominee."