U.S. stocks, which hit record highs Friday, are running up against some major headwinds, says Jim O'Neill, former chairman of Goldman Sachs Asset Management.

So if there is to be a global stock market rally this year, it will have to be led by other countries, he told CNBC.

"I think the [U.S.] market has got a number of challenges. One, it is very high in value. And if we get better data, Fed worries come straight back after a few days. Bond yields go up, and equity markets have got to compete with that," O'Neill said.

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The trailing price-earnings ratio on the S&P 500 totaled 17.7 as of March 28, according to Birinyi Associates.

"If we are going to have a global bull market this year, it will be led by something other than the U.S. That is possible," O'Neill said.

Emerging markets, particularly, China and India, and Germany could lead stocks higher, he said. "India has got this incredible potential that comes from its demographics," he said. And Germany is "trying to give a bit more leadership to the mess known as Europe."

Star bond investor Jeffrey Gundlach, CEO of DoubleLine Capital, casts doubt on U.S. stocks too.

"If you believe [Fed Chair Janet] Yellen is signaling the end of low rates, stocks are vulnerable," he told MarketWatch.

Yellen said in her press conference last month that the Fed may raise short-term interest rates about six months after it ends its bond purchases.

At this rate of tapering, the quantitative easing may finish as soon as October. That could put a rate hike in April, earlier than market watchers had forecast.

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