U.S. aid to Pakistan was terminated at midnight last night because of a procedural tangle in Congress and Pakistani nuclear developments, creating a new period of uncertainty in one of this country's most strategic relationships overseas.

At the beginning of the fiscal year -- 12:01 this morning -- the Reagan administration's 6-year-old waiver for Pakistan of U.S. nuclear laws expired, making new aid commitments to Pakistan illegal without enactment of a new waiver.

State Department spokewoman Phyllis E. Oakley expressed concern that the cutoff, which may or may not be temporary, "sends the wrong signal about the continuing U.S. commitment to Pakistan's security." She expressed hope that Congress will act quickly so that aid can be restored.

Congressional sources said floor fights in both chambers are likely this month and in early November over whether to resume the multibillion-dollar aid program, one of the largest in the world, and if so, under what conditions.

Rep. Stephen J. Solarz (D-N.Y.), a key figure on the issue in the House, said it will be a classic congressional struggle between competing objectives: "Whether we attach more importance to our nuclear nonproliferation objectives or to the support of our Afghanistan policies."

Pakistan is on the front-line against Soviet-dominated Afghanistan and is crucial to the massive military supply effort to the anti-Soviet Afghan rebels. After nearly eight years of war, the diplomatic and military aspects of the Afghan struggle seem to be coming to a head, with increasing pressure on the Soviets to get out of Afghanistan and increasing internal and external pressure on Pakistan to end its role in the Afghan resistance.

At the same time, Pakistan's longstanding drive to acquire nuclear weapons has reached the point that U.S. officials virtually concede Pakistan has the capability of making a bomb. The United States and other "nuclear supplier" nations have worked for a decade to slow or stop the Pakistani drive.

Making matters more difficult for Congress and the executive branch was the mid-July arrest in Philadelphia of a Pakistani native, Arshad Z. Pervez, on federal charges of seeking illegally to export nuclear-related equipment from the United States to Pakistan. This would appear to be in direct violation of a 1985 law sponsored by Solarz requiring a cutoff of U.S. aid to a nonnuclear nation such as Pakistan that seeks illegally to obtain U.S. nuclear equipment.

U.S. intelligence also has reported that Pakistan has violated a 1984 pledge to President Reagan not to enrich uranium more than 5 percent, which is sufficient for nuclear power plants and other civilian uses but not for weapons. Pakistan is reported to be enriching uranium at its secret Kahuta plant near Islamabad at a level approaching 95 percent.

The arrest of Pervez could hardly have come at a worse time for U.S. policy-makers. The 6-year-old waiver of a U.S. antiproliferation law, known as the Symington amendment, was expiring last night and a new, six-year, $4 billion U.S. aid program to Pakistan was to begin today if Congress approves.

Before the Pervez arrest, both the Senate Foreign Relations Committee and the House Foreign Affairs Committee had adopted two-year waivers of the Symington amendment that would permit the new aid program to begin. But after the arrest, Solarz and several key senators shifted to a much tougher stand, demanding that Pakistan forgo key elements of the nuclear weapons drive in order to continue receiving U.S. aid.

Undersecretary of State Michael H. Armacost, in a visit to Islamabad in early August, urged Pakistan to take major actions, including a verifiable cutback in the level of its nuclear enrichment program, to assuage U.S. antiproliferation concerns. Pakistan refused, considering the nuclear program a highly sensitive matter of national prestige and defense against its nuclear-capable neighbor, India.

Pakistani officials made it known recently that Pakistan will pledge not to make an explosive device and not to have a nuclear detonation. The Pakistanis also said they would ratify the 1963 Partial Test Ban Treaty, forswearing nuclear tests in the atmosphere, which Pakistan signed long ago but never ratified.

Pakistan has tied any future nuclear moves to equal moves by India. There is no sign that India is ready to take such actions, especially because failure to do so could continue the unstable situation in U.S. relations with Pakistan.

A new argument in the hands of the administration is a Central Intelligence Agency estimate that cutting off U.S. aid would not stop Pakistan's drive to obtain a nuclear weapons capability and would set back the U.S. antiproliferation effort by showing it to be ineffective.

Oakley said yesterday that "the Pakistanis understand that acquiring a nuclear explosive device would have the most serious consequences for our relationship and have assured us that they do not intend to develop nuclear explosives."

Despite these assurances, she said, a diplomatic dialogue continues on ways to allay U.S. nuclear concerns while maintaining U.S.-Pakistan security relations.