Back in 1968, when President Nixon was looking for economic advisers, Republican Alan Greenspan wisecracked: "You can cram into a telephone booth all the Republican economists qualified to be chairman of the Council of Economic Advisers, and still leave room for Fats Waller."

With a grin, Greenspan now notes that "times have changed -- there are lots more economists."

To be sure, the number of economists has proliferated enormously in the past 10 or 12 years, multiplying the availability of manifestly qualified Republicans. Moreover, with the country's swing rightward, conservative Republican economists of most kinds -- possibly excepting the gold nuts -- have been able to come out of the closet. It is the liberal Democratic Keynesians who have gone into hiding.

Now that President Reagan, after a slow start, has pretty much completed his selection of economists and economic advisers, it may be time to take a look at them as a group. Reagan's economists have one unifying characteristic: They all are conservative, anti-Keynesian, and profess devotion to a free-market, free-trade philosophy.

But they are for the most part a curious mix of supply-side tax-cutters, (who care little about anything except reducing rates in the high tax brackets -- and if the budget deficit swells, so be it,) and monetarists, (who care little about anything except inducing the Federal Reserve to follow a policy guaranteeing steady, stable growth in the money supply -- and if interest rates skyrocket, so be it.)

Treasury Secretary Donald Reagan -- two of whose principal aides are Undersecretary for Monetary Affairs Beryl Sprinkel, one of the nation's best-known monetary theorists, and Undersecretary for Tax Policy Norman Ture, a committed advocate of supply-side tax-cutting -- has wailed publicly: "I sometimes feel like I'm a referee."

The other main influence among Reagan's economists comes from what might be called the "deregulation school," chief exponents of which are Economic Council Chairman Murray L. Weidenbaum and a fellow CEA member, William A. Niskanen Jr. Weidenbaum personally is dedicated to reducing what he has said for years is rising government involvement in the private sector. In the blunt terminology of Reagan political types such as White House counsellor Ed Meese and Office of Management and Budget Director David Stockman, that means shrinking the size of the government.

The monetarists, led by Sprinkel, are aided and abetted by OMB staff aide Lawrence Kudlow, and OMB consultant John Rutledge, whose Claremont Economics Institute monetarist model of the economy has been used by the administration as the basis for its economic forecasting. Their force will be bolstered shortly by the third member of the CEA team, an absolutely pure monetary theorist named Jerry Jordan who sharpened his ideology at that most pristine of monetarist centers, the St. Louis Federal Reserve Bank. Thus, the monetarists have a foothold in the Treasury, OMB and CEA.

The supply-sides are concentrated in the Treasury, where tax policy is supposed to be crafted. There is Ture, in a post upgraded from the assistant secretary level, Assistant Secretary John Chapoton and Assistant Secretary for Economic Policy Paul Craig Roberts, a former Wall Street Journal editorial writer and dedicated supply-sider who sees red at the very mention of the word "Keynesian."

It is more difficult to categorize two high State Department officials who are critical in formulating foreign economic policy. Myer Rashish, a trade expert named to be undersecretary of State for Economic Affairs appears to be a pragmatist who has switched to the Republican side.

Like the Treasury's Ture, he once served on a John Kennedy task force. Rashish's assistant secretary Robert Hormats, who worked for the Nixon, Ford and Carter administrations, fits the mold of the skilled European civil servant more than anything else. Rashish and Hormats are likely to be voices of moderation in the Reagan camp.

Other forces for compromise in Reagan's world of economic extremism include Weidenbaum and White House assistant for policy development Martin Anderson. To be sure, no one on the Reagan team would confess any Keynesian taint; (Sen. Pete Domenici (R-N.M.), head of the Senate Budget Committee, forced an apology from the Wall Street Journal, which needled him with an editorial headline: "John Maynard Domenici." The senator wrote to assure that he was not now, and never had been, a Keynesian.)

But Weidenbaum at least has used the famed economist Alfred Marshall's line to the effect that there are "two blades to the economic scissors, supply and demand," and early in the game successfuly fended off efforts to translate the entire rationale for the Reagan program into a simplistic supply-side primer written by George Gilder.

Recently nominated to a nonpolicy-making post as assistant Commerce Department secretary for economic affairs, Robert Dederick, chief economist of the Northern Trust Co. of Chicago, is said to be eclectic rather than a monetarist or a Keynesian.

Anderson, who has had the longest and closest connection of all these people with Reagan, is a very conservative economist, a classic libertarian like Greenspan who doesn't drift into either the supply-side or monetarist extremes. He is close to Weidenbaum on big-government issues and maintains a bridge to more traditional Republican economists such as Arthur Burns (for whom he once worked).

So far, the biggest test of economic ideology in the Reagan administration is being decided in something very basic: whether the free-market, free-enterprise underpinning will be able to stop the onslaught of politicians in the Reagan cabinet who push for limits on Japanese auto imports. The older-school Republican economists on Reagan's outside advisory committee once thought (as did Anderson) that they had that fight won. But free-market words are being undercut by the most transparent kind of protectionist arm-twisting on the scene in Tokyo.

As for the monetarists and the supply-siders, the tests for purity are coming in contests with the Fed, and on the floor in Congress, where certain old-fashioned Republicans still worship at the balanced budget altar. It is clear that the supply-side Kemp-Roth bill will have to be modified to get enough Republican senators, concerned with budget deficts, to vote for the Reagan program.

It's sure tough, Meesrs. Sprinkel, Ture, Roberts, et al. But then, who promised you a theological rose garden instead of the real world?