The US Dow Jones index broke through the 16,000 level for the first time on Monday before giving up some of the gains in late trade.
At one point the Dow touched 16,030.28, but it ended 14.32 points up on the day at 15,976.02.
The S&P 500 index rose above 1,800 for the first time, before a late sell-off pushed it down 6.65 points to 1,791.53.
Stocks have been buoyed by hopes that the US central bank will continue with its economic stimulus programme.
The cheap money policy keeps interest rates low, which means investors are driven to find investments – such as shares – where they hope to find higher returns.
However, billionaire investor Carl Icahn told the Reuters news agency that he was “very cautious” on equities, adding that markets could see a “big drop”.
Shares in Boeing rose 1.7% following news at the weekend that it had booked about $100bn (£62bn) in orders at the Dubai airshow.
But shares in social networks had a tougher day. Twitter fell 6.5% to $41.14 following a downgrade by Wunderlich Securities. Facebook’s stock also dropped 6.5%.
Although the current chairman of the Federal Reserve, Ben Bernanke, is leaving the post, Janet Yellen, who is all but certain to take over from him, is expected to keep the money flowing while the US economy remains fragile.
Ms Yellen has said the Fed’s the current extraordinary bond-buying efforts “certainly would continue for the foreseeable future”.
She added that she does not see signs of a US stocks bubble.
“Financial markets are buoyed by Janet Yellen’s comments at her confirmation last week, which re-iterated a dovish policy message from the Fed,” said Neil MacKinnon of VTB Capital.
Earlier this month, it was announced that the US economy grew at a better-than-expected annual pace of 2.8% in the third quarter.
However, the latest figures also showed that the unemployment rate edged up to 7.3% from 7.2% in September.
The world’s largest economy is not thought to be on solid enough ground to withstand the shock that could be caused by a change in policy.
Earlier, global shares were helped by rises in the Chinese stock market following announcements over economic and social reforms, including an intention to relax the one-child policy and abolish the controversial labour camp system.
China’s Shanghai Composite rose by 2.9% and Hong Kong’s Hang Seng index climbed 2.7%.