The International Court of Justice — founded in 1945 to rule on legal disputes between nations — announced late Friday dates for separate hearings for the three cases between March 7 to 16.
In the cases brought against India and Pakistan, the court will examine whether the tribunal based in The Hague is competent to hear the lawsuits.
The hearing involving Britain will be devoted to “preliminary objections” raised by London.
A decision will be made at a later date as to whether the cases can proceed.
In 2014, the Marshall Islands — a Pacific Ocean territory with 55,000 people — accused nine countries of “not fulfilling their obligations with respect to the cessation of the nuclear arms race at an early date and to nuclear disarmament.”
They included China, Britain, France, India, Israel, North Korea, Pakistan, Russia, and the United States.
The government based in the Marshall Islands capital of Majuro said by not stopping the nuclear arms race, the countries continued to breach their obligations under the Nuclear Non-Proliferation Treaty (NPT) — even if the treaty has not been by signed by countries such as India and Pakistan.
The Marshall Islands had decided to sue the world’s nuclear heavyweights as “it has a particular awareness of the dire consequences of nuclear weapons,” it said.
Between 1946 and 1958 the United States conducted repeated nuclear tests in the Marshall Islands, Majuro’s representatives said in papers filed in court.
But the court only admitted three cases brought against Britain, India and Pakistan because they already recognised the ICJ’s authority.
In March 2014, the Marshall Islands marked 60 years since the devastating hydrogen bomb test at Bikini Atoll, that vapourised an island and exposed thousands in the surrounding area to radioactive fallout.
The 15-megaton test on March 1, 1954, was part of the intense Cold War nuclear arms race and 1,000 times more powerful than the atomic bomb dropped on Hiroshima.
Bikini Islanders have lived in exile since they were moved for the first weapons tests in 1946.
When US government scientists declared Bikini safe for resettlement, some residents were allowed to return in the early 1970s.
But they were removed again in 1978 after ingesting high levels of radiation from eating local foods grown on the former test site.
The Marshall Islands Nuclear Claims Tribunal had awarded more than $2 billion in personal injury and land damage claims arising form the nuclear tests, but stopped paying after a $150 million US compensation fund was exhausted.
Eight of the nine countries originally targeted in the lawsuits have officially admitted to possessing a nuclear weapon. Israel has never acknowledged having one, but observers believe it is the sole nuclear-armed nation in the Middle East.