Washington, the city of cenotaphs, is running out of monument space.

Less than a dozen "choice spots" are left in downtown Washington, says the National Park Service. And even though Washington has more bronze generals on horseback, stone statesmen, memorials and fountains than any other city in America, memorial makers already are eyeing those "choice spots" for more monuments.

The Park Service, which 10 years ago proposed a moratorium on monuments in Washington, now sees an end to the era of major memorials here, simply because there soon will be no more room.

"The 'cemetery' is full," one Park Service official commented dryly, unless the Mall and East and West Potomac Parks are opened for statutory, which the Park Service opposes. However, there remain 75 "less choice" spots for small monuments away from downtown, primarily on traffic islands and street corners east of the Capitol.

Congress has authorized several new downtown monuments, including a memorial to Gen. John J. Pershing on Pennsylvania Avenue, a small memorial to the 56 signers of the Declaration of Independence on an island in Constitution Gardens, the American Legion Freedom Bell (an 8-ton copy of the Liberty Bell) outside Union Station and the largest, costliest memorial in the nation's history: the 1,000-foot, $46 million garden wall of waterfalls planned for the west end of the Tidal Basin in honor of Franklin D. Roosevelt.

Many memorials once on the Mall and downtown streets have been removed during construction projects and are in cold storage at various warehouses. If permanent resting places can be found for them, they will rejoin more than 500 other statutes, tombs, temples, urns, busts and other bronze and stone memorabilia decorating Washington parks.

Among the displaced monuments are the marble 1928 Cuban-American Friendship Urn, a bronze memorial to the inventor of photography, Louis Daguerre, a marble statue of Union Gen. George Meade on his horse and a fountain honoring Sen. James McMillan, who led the turn-of-the-century restoration of the Mall. In 1901, McMillan complained that the demand for memorials in Washington "has reached the acute stage," and tried to set up a system for screening and placing memorials. He failed.

The Park Service also is struggling still with a 1976 congressional directive to chisel the names of the two newest states -- Alaska and Hawaii -- on the Lincoln Memorial or to commemorate them in some other noticeable way at the nation's most visited memorial.

And waiting in the wings are several other large memorials:

A "Holocaust" memorial to the six million Jews killed by the Nazis, authorized by President Carter last spring. A presidential commission has been formed to determine what kind of memorial should be built and where it should go.

A new Navy memorial, possibly a concert shell for the Navy Band set inside a wave sculpture. The memorial is being proposed in Congress as a general commemoration of those who have served in the Navy. But the Park Service is not enthusiastic because officials feel the existing Navy and Marine monuments, in a city where military memorials already outnumber all other kinds, are sufficient statutory reminders of the Navy's contribution to the country. The Navy now has a Peace Monument at the foot of Capitol Hill, the Navy-Marine sea gull monument on Columbia Island and the Seabees memorial in Arlington Cemetery, as well as a number of monuments to individual admirals and commodores.

A controversial proposal for a memorial to Yugoslav General Draza Mihailovich, whose partisan forces rescued 500 U.S. airmen shot down during World War II. Bills authorizing the memorial, backed by the airmen and their families, have been introduced in Congress since 1975. But the plan is opposed by Yugoslav President Marshal Tito and the State Department. Mihailovich was executed on Tito's orders after the war.

A statue of Albert Einstein is planned opposite Constitution Gardens on the front lawn of the National Academy of Sciences. The statue, which would be three times lifesize, will be on Park Service land that Congress transferred to the academy last year. Since the memorial will be a private statue, it is not subject to the same reviews as public statues.

Numerous other memorials have been proposed in Congress, including some that were authorized as much as 40 years ago but have not been built because the sponsors never raised the money. For instance, a statute of Peter Muhlenberg was approved in the '30s for the traffic triangle at Connecticut Avenue and Ellicott Street NW. The triangle is still reserved for a memorial to Muhlenberg, a Revolutionary War statesman, clergyman and soldier.

A monument to veterans of the Vietnam War, to POWS of that war or those missing in action has been proposed almost every year since the war ended. Under one bill, 56,244 trees would have been planted on the Mall, one for each U.S. soldier killed in Vietnam. But Park Service officials objected, pointing out that the memorial would have created a forest on the Mall.

One monument that frequently has been proposed in Congress is a $1 million National Law Enforcement Heroes Memorial. However, it apparently has been dropped since it was deemed not of "outstanding national or international significance" by the National Capital Memorial Advisory Committee.

The committee, established in 1976, advises the secretary of Interior on the appropriateness of memorials being proposed in Congress, since Interior is invited to comment on such bills. If Congress approves a memorial, the committee, composed of federal and local officials, then suggests what the memorials should look like and where they should go.

Getting a monument or cenotaph -- a memorial to a person buried elsewhere -- in Washington has been more difficult since the committee was created. (Some memorials, however, like the relatively noncontroversial bust of retired Supreme Court Justice William O. Douglas, have had relatively easy going. That bust, placed on the C&O Canal last year, "sailed through in only three weeks from start to finish," said John Parsons, committee chairman and an associate regional director of the Park Service.)

A model memorial bill suggested by the committee and now generally used in Congress allows Interior, in conjunction with the National Capital Planning Commission and the Fine Arts Commission, to decide the design of a monument and where it should go. In addition, the bill suggests that monuments be privately funded.

Most memorials proposed or built recently have been funded privately, although the Park Service will maintain them. However, the proposed Navy, Vietnam and police heroes memorials would be federally funded, and the memorial to the signers of the Declaration will be paid for with $350,000 left from the Bicentennial Administration.

The proposed FDR memorial, approved but still to be funded by Congress, would be, by far, the most expensive. It also would cost more to maintain than any other U.S. monument; Park Service officials estimate about $1.2 million a year a minimum level, which means turning down the waterfalls and lights at night.

While a memorial to FDR has been proposed, and has been controversial, for more than two decades, it shows how difficult it has become, even for a president, to get on the Mall. Only 10 other presidents have statues in Washington, compared with more than 40 generals.

Former Interior secretary Stewart L. Udall said more than 15 years ago that one way to help end Washington's "monumental chaos" would be to stop building memorials to our contemporaries -- whom history may later judge unworthy of memorializing. Dozens of memorials around the Nation's Capital stand in stony tribute to that proposition, say Park Service officials.

On the Ellipse, beside the White House, is the Butt-Millet Memorial, erected by the friends of two Washingtonians who went down on the Titanic -- for which there is a separate memorial on Maine Avenue.It is one of many memorials, says Parsons of the Park Service, unlikely to be erected in Washington, if the decision were made today, and it is one which might be a candidate for removal.

After all, he points out, dozens of monuments here have been moved, and even General Meade is in cold storage.