Theodore Roosevelt urged the United States to "speak softly and carry a big stick." Ronald Reagan's corollary seems to be ". . . and use that stick to rap knuckles." Nowhere has this policy worked better than in the dusty recesses of the United Nations.

The flamboyance of the General Assembly seems a long way from the quiet activities of U.N. specialized agencies, but in two of these, the International Labor Organization and the United Nations Educational, Social and Cultural Organizations dramatic events have taken place.

The ILO, a unique organization composed of representatives of government, labor and business, aims toward "the creation of more jobs, in a climate of sound industrial relations, based on full respect for basic human rights and freedoms." But in recent years, these goals, fully supported by the U.S. government, the labor movement and the business community have played second fiddle to more political ones.

Part of the problem arose when the U.S.S.R. joined in 1954. The communist system allows no distinction between labor, employers and government, so the uniqueness of the ILO was put to a test, and the East bloc moved quickly to distort its original thrust. The autonomy of workers' and employers' groups was attacked; Soviet violations of conventions on freedom of association were ignored, political polemics raged, and committee packing with East-bloc members was attempted.

Politicization of the ILO took place in 1974 in another area as Arab and African states, with the gleeful support of the U.S.S.R., condemned Israel for alleged racism and discrimination, without waiting for the results of an investigation into the matter, thus shredding the concept of due process. In 1975, the PLO was admitted as an observer, and U.S. patience, with AFL-CIO President George Meany as its goad, ran out. Secretary of State Henry Kissinger in accord with ILO procedures, sent a letter of intention to withdraw within two years unless changes were made. In 1977, President Carter took us -- and our 25 percent contribution to the ILO budget -- out.

The results were quick in coming. No bureaucrat, international or otherwise, likes to see his empire crumble. In 1978, the ILO criticized the Czechs for discrimination in employment. In 1979, the ILO questioned the Soviets on human rights violations. Secret ballots were adopted in certain ILO proceedings. An anti-Israel Arab-sponsored resolution was defeated in 1978 and none was introduced in 1979.

Although the organization was scarcely perfect, by May 1980, the United States felt sufficiently satisfied to rejoin, remaining vigilant against any new deviation. To date, this judgment seems justified, particularly in light of the fact that the Poles have recently announced their intention to withdraw in the face of ILO criticism of violations of freedom of association.

In the case of UNESCO, the United States criticized UNESCO's statist approach to development; the extraneous politicization of almost every subject dealt with; its blatant disregard for the opinions of the Western democracies, which provide more than 70 percent of its budget; irregularities in its bureaucracy; and, the focus of the most attention, attacks on freedom of the press, with calls for licensing of journalists and the press seen as governmental lap dogs. In December 1983, the United States gave notice of its intent to withdraw. Director General M'Bow tried to pass this off as an isolated, typically Reaganite action. But a week ago, when Great Britain decided to join the United States, it was a stunning blow. The two nations contribute about a third of the ILO budget. Proponents of a strong approach have now been reinforced, the likelihood of other countries joining in is increased, and the hope for reform strengthened.

One fact has been overlooked: the United States intends to spend its UNESCO monies on projects in other agencies such as the U.N. Development Program and the OAS, where overhead (80 percent at UNESCO) is not so high and the dollar goes further.

Some critics of the U.S. and British moves say if we do not play in the UNESCO game, we cannot influence the organizations. Others say the Third World countries will become spiteful and angry and will thwart reforms out of pique.

Yet Lane Kirkland, current AFL- CIO president, feels there is "nothing wrong with objecting when your own money is used to subvert human values you stand for." And Jeane Kirkpatrick, U.S. ambassador to the U.N., feels that in both the ILO and UNESCO, "organizations were twisted to serve values antithetical to their own charters and to human freedom." She adds: "The ILO experience demonstrates that U.S. departure from a U.N. organization isn't necessarily forever. ILO reforms returned it to its original purpose."

In short, it seems clear that a willingness to stand for principle and to call a halt to hypocrisy pays off. It is not only psychically satisfying: it works.