Spurred by the staging of what's claimed to be the biggest disarmament rally in US history, plans are being made for a whole new series of protests and behind-the-scenes efforts aimed at ending the nuclear arms race.
''This is just the beginning,'' said US Rep. Edward J. Markey (D) of Massachusetts, just before he rose to address a cheering throng, estimated by police at about 500,000, in the 18-acre Great Lawn of New York City's Central Park. (Police estimated another 250,000 people might have taken part in other events leading up to the Central Park rally.)
''This issue (of nuclear disarmament) has the staying power, 'the legs,' to be the most powerful issue in the world,'' added Representative Markey.
''The rally is going to send a very powerful signal to Washington. This is not just a radical movement. It has a has a middle-class base. . .''
The rally did draw from a fairly wide cross section of people. There were a number of long-time anti-war activitists, such as Abbie Hoffman and Coretta Scott King, widow of the late Martin Luther King Jr. But there were others, too - ranging from church leaders to New York actors to children attending their very first political demonstation. However, some who attended said they were protesting as much against the cut in federal jobs programs and high unemployment as much as against nuclear weapons.
Now many of the rally's organizers and speakers are looking ahead for ways to keep their national campaign for a freeze and reduction of nuclear weapons worldwide alive and growing. They are already planning another massive rally on October 15 - just three weeks before this year's Congressional elections - to take advantage of what they maintain is a rising tide of anti-nuclear sentiment in the US.
In addition, Markey - along with other federal lawmakers - have a more immediate hope that the energy and convictions expressed so vociferously and colorfully in New York's Central Park will generate new support in Congress for a nuclear weapons freeze. So far, some 171 House members have co-sponsored legislation calling for a freeze.
And, yet, while it may be a substantive springboard, the rally here will not have any major impact on US weapons strategy in the foreseeable future, according to Defense Secretary Caspar Weinberger. In a public television station interview taped the day before the rally, Weinberger acknowledged that although the rally ''is certainly something people will notice, I don't think anybody rushes back and says, 'We have to change our policy.' ''
Many of the demonstration's organizers conceded that such a policy change will not come quickly or, for that matter, easily.
''There are long and difficult years ahead before we find nuclear disarmament and peace,'' Espiscopal Bishop Paul Moore Jr. of New York told more than 10,000 people at an interfaith service at the Cathedral of St. John the Divine June 11.
One notable thing about the American campaign for nuclear disarmament, according to many observers as well as participants here, is that the movement has fairly ''exploded'' in the last few months. And, as a result, it seems to lack some of the organization and internal discipline of earlier mass movements.
Coretta Scott King, one of more than a score of speakers at the rally, told the throng ''somewhere along the line we got complacent.''
''So we have to start again,'' she continued, ''We have to send a message to Capitol Hill and the White House that we need peace with justice and justice with peace.''
Glen Alcalay, a spokesman for the National Association of Atomic Veterans, which is composed of US servicemen who witnessed atomic bomb-testing in the Pacific and elsewhere in past decades, said the American peace movement only really began to gather momentum in the last several months following anti-nuclear demonstrations in Europe last fall.
''What happened in the past six months,'' Alcalay contends, ''is that many people began to have a growing feeling of helplessness'' in the face of the prospect of a seemingly endless build-up of nuclear arsenals here and in the Soviet Union. Then, according to a wide cross section of rally participants, this feeling of helplessness was fueled by smaller scale rallies in this country.
Too, a number of groups appear to have jumped on the anti-nuclear bandwagon because of the considerable costs involved in sustaining a nuclear buildup. These costs are perceived to be at the expense of federal social and job programs. That helps to explain, for example, why Local 1199 of the National Union of Hospital and Health Care Employees and the Coalition of Black Trade Unionists recently joined long-time activist Rev. William Sloan Coffin of Riverside Church in condemning the nuclear arms race.
Besides preparations for another major rally October 15, these other demonstrations and events are planned to keep the anti-nuclear momentum going:
* On Monday (June 14), in New York City, protesters plan to blockade various missions to the United Nations, including the Soviet, Israeli and South African missions. But organizers promise that although they expect many demonstrators to be arrested outside the missions, their protests will be peaceful. (Indeed, police reported no untoward incidents over the course of the June 12 rally.)
* Also in New York, on June 17, anti-nuclear supporters plan a massive protest outside the United Nations, where President Reagan is scheduled to speak at the special session on disarmament. It isn't known exactly how many will assemble outside the UN, but the figure could number in the thousands since many June 12 rally participants say they plan to stay in town until then.
* In Washington, members of the Children's Campaign for Nuclear Disarmament (CCNA), which claims an estimated 5,000 active supporters, will assemble outside the White House to read aloud thousands of letters from children expressing their concern about nuclear weapons. In addition, CCNA representatives expect to speak in schools across the country this fall, with the hope that the students will help persuade their parents to be more concerned about the nuclear arms build-up.
* Several states, including New Jersey and Wisconsin, have approved legislation calling for non-binding state voter referendums on a US freeze in nuclear weapon levels. Several other state legislatures are considering similar action.