NEW YORK (CNN/Money) - Some day, the Maestro will put down his baton.

Federal Reserve Chairman Alan Greenspan turned 76 in March, his term is scheduled to end on June 20, 2004, and he has served for nearly 15 years, the second-longest tenure in Fed history.

He is probably not going anywhere for a while -- his health seems fine, no one doubts that he loves his work and the economy is just recovering from a recession, certainly an awkward time to introduce a new Fed chair to the job.

But it's not too soon to speculate about his replacement, especially since that person is probably someone who's already relatively well-known, at least in economic circles.

"The Fed chairman needs to be able to generate confidence in the economic and financial leadership of the country, not to grow into it, but to have it instantaneously," said Andrew Brimmer, a Fed governor from 1966 to 1974 and current president of Brimmer & Co. in Washington, D.C. "Remember, that person will be judged inevitably against the stature of Alan Greenspan."

And that is certainly a tall order. Thanks in part to his deft reaction to crises such as the 1987 stock-market crash, which happened just months after his appointment by President Reagan, Greenspan became a household name, and Wall Street came to hang on his every inscrutable word.

Great pressure will also be on President Bush, who will nominate the next chair for approval by Congress. It will probably be one of the most important decisions he makes, since the Fed, by manipulating the supply of money and interest rates, directly affects the degree of inflation and growth in what is easily the world's largest economy.

Fed policy makers are scheduled to meet Tuesday to discuss their target for short-term interest rates, and they are almost certain to leave them unchanged. To fight a recession that likely began in March 2001, the Fed slashed its target for the federal funds rate, an overnight bank lending rate, 11 times last year to 40-year lows.

The central bank has left rates alone so far in 2002, and there was speculation earlier in the year that the Fed could start to raise them as soon as next week to keep the economy from overheating and fend off inflation.

But economic data in recent weeks, including Friday's jump in unemployment, have put the strength of the recovery in doubt, and Greenspan and other Fed officials have made it abundantly clear they're in no hurry to raise rates. Most economists now think the Fed could wait until August before it starts to worry about inflation.

"A cut next week is completely off the table, and the chance of a June move is no better than 50/50," said former Fed economist Wayne Ayers, now chief economist at Fleet Boston Financial. "By August, they will know a whole lot more about the economy than they do now, and they will also have a better picture of the geopolitical situation -- that's got to be on their minds as well."

One of the skills of a Fed chairman is the ability to break the news of rate hikes gently to Wall Street, which hates high interest rates. They make the cost of borrowing steeper, cutting corporate profit margins and discouraging consumer spending, which fuels two-thirds of U.S. gross domestic product.

The Fed's six interest-rate hikes in 1999 and 2000 brought Greenspan the toughest criticism of his career. The increases were designed to put the brakes on the economy and possibly helped pop two speculative bubbles -- one in Nasdaq stocks and the other in spending by businesses on new technology and productivity improvements.

The bursting of the Nasdaq bubble cost investors billions at about the same time oil prices surged, hitting corporate profits and consumers' wallets. The result was a sort of "perfect storm" that led to the economy's first recession in a decade.

Of course, just to show that you can never please everybody, Greenspan has also been accused of helping to make the speculative bubbles bigger in the first place by not raising rates early enough.

But much of the criticism of Greenspan was quieted when his quick action in the aftermath of the Sept. 11 terror attacks helped keep the economy from sinking into a deep recession.

The perception of the Fed chair as Master of the Universe is one of many things President Bush will have to keep in mind when he picks a candidate. He'll also want to pick someone with whom he thinks he can have a decent working relationship, especially considering the sometimes rocky history of presidents and Fed chairmen:

• President Truman nominated William McChesney Martin for the job in 1951 thinking he would do what the White House wanted him to do. Instead, Martin became a staunch defender of Fed independence.
• In 1969, President Nixon asked Martin to step down and become his Treasury Secretary, giving long-time Nixon adviser Arthur Burns the chance at the job. Martin refused, but Nixon announced that Burns would succeed him, several months before Martin's term actually ended.
• Supporters of the elder President Bush grumbled that Greenspan did not do enough to fuel the economy in 1992, and the sluggishness of the economic recovery that year contributed to Bush's defeat in the presidential election.

Related links       Who will be the next Greenspan? Federal Reserve Special Report: Eyes on the Fed

"The selection of a Fed chairman is not easy because you really have to be able to satisfy so many groups, get the nomination through Congress, have international backing, pick somebody well-known in the United States and pick somebody with views that are flexible," said Allen Jacobson, senior vice president and political analyst at Washington Analysis. "And, of course, the political party in power would like to appoint someone of their own."

Click here for a discussion of some of the likely candidates.