The Senate Foreign Relations Committee hearing is titled Authority to Order the Use of Nuclear Weapons.
The chairman of the panel accused President Trump last month of setting the US “on a path to World War III”.
In August, Mr Trump vowed to unleash “fire and fury like the world has never seen” on North Korea if it continued to expand its atomic weapons programme.
The last time Congress debated this issue was over a four-day hearing in March 1976.
A nervous laugh
Senator Chris Murphy, a Connecticut Democrat, explained the reason for Tuesday’s public hearing.
“We are concerned that the president is so unstable, is so volatile, has a decision-making process that is so quixotic, that he might order a nuclear-weapons strike that is wildly out of step with US national-security interests.”
Senators also wanted to know what would happen if the president ordered a nuclear strike.
Robert Kehler, an ex-commander of US Strategic Command, said that in his former role he would have followed the president’s order to carry out the strike – if it were legal.
Mr Kehler said if he were uncertain about its legality, he would consult with his own advisers.
Under certain circumstances, he explained: “I would have said, ‘I’m not ready to proceed.'”
One senator, Ron Johnson, a Republican from Wisconsin, asked: “Then what happens?”
Mr Kehler admitted: “I don’t know.”
People in the room laughed.