New York ? The bull market is back, according to some definitions of the term at least.

The Standard & Poor’s 500 index this past week posted its best quarterly gain since late 1998. Wall Street’s three main gauges are at their highest levels in a year. Investors are more upbeat that an economic rebound, three years in coming, is now under way.

Still, the bull market label gives investors a false hope of future, sustainable gains, according to experts.

“I’ve seen a concrete definition of a bear market as being down 20 percent, so for bull markets you could say it means rising 20 percent,” said Robert Shiller, a Yale economics professor and author of “Irrational Exuberance,” which correctly predicted in 2001 the bursting of the tech bubble.

“But it’s often misleading to call something a ‘bull’ or a ‘bear’ market, because people think you’ve diagnosed something, when in fact all you’ve given it is a name,” he said. “What they think it means is that it’s going to continue.”

Indeed, some experts define a bull market as a 20 percent upward move over any time period, while others prefer to see the gain sustained over several months to a year. A small minority refuses to declare a bull market until stock gauges reach a new peak.

There also are “cyclical” bull markets, which run for about a year, compared to multiyear “secular” ones.

Many experts believe Wall Street’s current run can be best described as a cyclical bull market within a secular bear market, which began in 2000. Historically, secular markets last about 10 to 15 years, according to Ned Davis Research in Venice, Fla., so stocks could well return to bearish declines in a year or two, if not sooner.

Stocks have already gone through a cyclical bull market recently. Prices rose more than 20 percent from September 2001 to March 2002 following the Sept. 11 attacks. A flurry of accounting scandals, however, soon derailed that rally and stocks eventually fell to multiyear lows on Oct. 9, 2002.

In the current bull market run since Oct. 9, the Dow has advanced about 24 percent, the Nasdaq is up 49 percent, and the S&P has gained 27 percent.

Sam Burns, research analyst at Ned Davis, said some analysts question whether stocks are in a longer-term bull market because there is still a great deal of economic uncertainty. For example, the unemployment rate remains high, shooting up to 6.4 percent in June; the report sent stocks moderately lower Friday.

Still, optimism is high. On Monday, the S&P closed the second quarter with a 14.9 percent gain, the highest since 1998.

The Dow and Nasdaq claimed their best quarter since late 2001, rising 12.4 percent and 21 percent, respectively.