MOSCOW, JULY 27 -- Byelorussia today became the latest Soviet republic to declare its sovereignty amid signs of severe new economic and nationalist strains around the country that could test the authority of President Mikhail Gorbachev.

In addition to asserting the primacy of Byelorussian laws over those of the Soviet Union, the legislature of Byelorussia, a republic with a population of 10.2 million, proclaimed its wish to become a neutral, nuclear-free state with its own armed forces. A similarly worded declaration was adopted earlier this month by the neighboring republic of Ukraine, with 51.7 million people.

So far, 11 of the Soviet Union's 15 republics have adopted sovereignty declarations of varying decrees of firmness, ranging from an outright declaration of independence by Lithuania to more cautiously worded assertions of the republics' rights. The remaining republics, all in Central Asia, are likely to follow suit over the next few months during negotiations for a new union compact.

Both the Byelorussian and Ukrainian declarations were adopted with the backing of the local Communist parties, an indication that the Soviet leadership in Moscow is now ready to accept a significant devolution of power to the republics. Under pressure from the republics, Gorbachev has agreed to a fundamental reshaping of the Soviet federation as the price for preserving a united market in trade and central control over the principal economic levers.

A more immediate concern for Gorbachev than the sovereignty declarations by the republics is the rapidly deteriorating state of the economy. Official figures released today showed that the Soviet Union's hard currency balance of payments deficit has more than doubled over the past year, reaching $11 billion for the first half of 1990.

This week, cigarettes became the latest consumer item in chronically short supply, producing long lines outside tobacco kiosks and triggering acts of protest in several industrial cities. A typical one took place in the Urals city of Perm yesterday when 1,000 angry customers blocked traffic along the city's main thoroughfare and formed a strike committee.

Within hours, the strikers' demands had expanded from the normalization of tobacco sales to the abolition of Communist Party cells at industrial plants. Soviet journalists reported that the protesters finally agreed to go home only after city officials promised to ship in 250,000 packs of cigarettes from army warehouses.

Such spontaneous outbreaks of unrest have become increasingly common here as one commodity after another becomes the object of panic buying. The shortages are likely to increase the pressure on the government to introduce drastic economic reforms, despite fears that price rises could lead to further strikes and demonstrations.

The imbalance in the market also has disrupted what otherwise promises to be an excellent harvest, causing peasants to withhold their grain from the state because of the lack of industrial goods. The Communist Party daily Pravda reported today that collective farm workers are forming strike committees in several regions of the country to demand improved supplies of fuel and equipment.

In an attempt to assert his authority, Gorbachev earlier this week issued a presidential decree giving nationalist groups 15 days to hand in their weapons. However, initial reports from Armenia, where the largest stocks of illegally held weapons are concentrated, suggest that it may prove very difficult to enforce the order without large-scale bloodshed.

The leader of the Armenian Liberation Army, Razmik Vasilyan, told Reuter that his group -- which, according to official estimates, has 20,000 supporters -- would refuse to hand over its weapons. "It is better to die than betray your people," he said.

At a press conference today, Interior Minister Vadim Bakatin said 4.7 million weapons are in private hands. The majority are hunting rifles, but the figure also includes more than 11,000 firearms seized from police stations and army units over the past few months.

Bakatin said responsibility for enforcing the presidential decree rests primarily with the governments of the republics. But he acknowledged that the Armenian legislature may refuse to endorse Gorbachev's order, in which case the Kremlin will have to decide whether to order a state of emergency in the republic and impose presidential rule.