When the heads of the U.S. and Marshall Islands delegations sit down today in New York to try to reach some understandings on a new compact of free association between their governments, the most difficult problem will be how to deal with the continuing health and environmental effects from U.S. nuclear weapons tests conducted in the islands more than 20 years ago.

In 1946 and 1947, when the United States ran the Marshalls as a trust territory, it removed the inhabitants of Bikini and Enewetak atolls so those island chains could be used for testing nuclear weapon designs.

Between 1946 and 1958, 64 nuclear shots were exploded on atoll islands and in lagoon waters.

The largest U.S. bomb ever detonated, the 15-megaton Bravo shot on Bikini March 1, 1954, sent measurable fallout more than 300 miles away and dosed Marshallese on at least two atolls.

Now, more than 20 years after the last nuclear test, the Marshalls have voted to become independent from the United States, and the trusteeship will end in 1981.

But what the new Marshallese secretary of foreign affairs, Anton A. DeBrum, calls the "legacy of nuclear contamination and disease from weapons testing" must still be resolved. For example:

The $100 million U.S. cleanup of the 2.75 square miles of Enewetak Atoll, site of 43 tests, has failed to reduce soil radiation enough in some northern islands to permit the safe growing of coconut trees, according to Department of Energy specialists. DOE has recommended that the Enewetak people, who are scheduled to return to the atoll next year after 30 years in exile, be prohibited from planting.

a DOE study of Bikini Atoll has found that the second-largest island in the chain will not be safe under criteria used at Enewetak "for about 20-25 years." Bikini Island last year was declared unsafe for the next 30 years and almost 100 Bikinians who had moved back were removed again.

Recent medical surveys at Rongelap and Utirik atolls, both of which were dosed by radioactive fallout from the 1954 Bravo shot, turned up additional thyroid nodules among the persons there. In the past, such nodules were traced to radioactive iodine in the fallout and were removed by surgery before they could turn cancerous. Almost half the 82 exposed Rongelap people have had nodules or some other health effect from the fallout.

An informal survey of Rongelap has turned up what Marshall Islands' officials call an "excessive" number of birth defects.

A recent Marshallese survey of Likeip Atoll has turned up thyroid nodules in persons who were there during the 1954 fallout. The atoll had not been thought to have received enough high-level fallout to cause long-term health effects.

A DOE medical team has been sent to coduct a more formal investigator at Likeip.

Beginning today, U.S. Ambassador Peter R. Rosenblatt, President Carter's representative for Micronesian status negotiations, and Marshall Islands Foreign Affairs Secretary DeBaum expect to deal with future U.S. health and radiation contamination responsibilities as well as compensation for past and present hardships.

Complicating the discussions are disagreements in both governments on how to deal with the questions.

Take Enewetak, as an example.Although DOE has opposed planting 18,000 coconut trees in the northern islands, the Defense Nuclear Agency, which has run the cleanup, favors it.

The Interior Department, which is responsible for administration of the trust territories, is stil studying the question. Some 23,000 trees are going into the southern Enewetak islands, where containination was much lower.

The new Marshallese government officials oppose former residents' returning to Enewetak next year as scheduled until the officials are convinced it is safe. But the Enewetak people, who have participated in arranging and carrying out the cleanup, want to go back to their home atoll even if some of it is considered still radioactive and threrefore risky.

Bikini Atoll presents an even more difficult situation, since the former residents cannot go back for at least 20 years.

Some Bikinians want to stay on Kili, a tiny Pacific island where they were relocated in the late 1940s. Others want to live temporarily on different Marshall atolls until Bikini si safe. A third group wants to be given land in Hawaii now owned by the U.S. government. A fourth group would like to go back to Bikini, even though it is not considered safe by U.S. environmental standards.

An additional complication is that several Marshallese groups were working on their problems long before the isalnd's independent government was created.

For example, the Enewetak, Rongelap and Utirik people years ago hired a lawyer, Theodore R. Mitchell of Micronesian Legal Services Corp., to work on cleanup and health matters. The Bikini people have hired Jonathan M. Weisgall of the Washington firm of Covington & Burling.

Mitchell prevented the Pentagon from blowing up an Enewetak island as part of a 1972 missile test experiment. He later was instrumental in getting the $100 million cleanup started.

Weisgall, when Bikini was being prepared for 1975 return, forced the United States to do the testing that led to findings that the atoll's key islands were still unsafe.

Both of these lawyers have more experience in Micronesian matters than does Richard D. Copaken , also of Covington & Burling, who was hired recently by the new Marshall Islands government.

Getting these men to agree on a common position may become a problem.

For example, Mitchell took the initiative on future U.S. health and environment care for the islands and their inhabitants by getting Rep. Phillip Burton (D-Calif.) to introduce legislation on April 26 that would provide regular radiological surveys of the atolls and comprehensive health care for the exposed islanders and their descendants.

Burton is chairman of the House Interior subcommittee that handles trust terriory legislation.

The measure passed the House May 7 and went to the Senate. Should it pass there and be signed into law by the president it would take precedence over any health care solution worked out in the current government-to-government negotiations.