By any normal yardstick Syria is virtually bankrupt. But ordinary rules rarely apply to this pivotal Middle East country renowned for juggling with a variety of ways to address its problems.

Still, so pressing are the economic problems that officials no longer dismiss out of hand persistent rumors that Syria may accede to longstanding requests from oil-producing Arab states on the Persian Gulf to loosen ties with ally Iran and improve relations with their mutual arch-enemy, Iraq.

Further complicating Syria's worst economic squeeze since President Hafez Assad assumed power in 1970 are antigovernment terrorism at home, accusations of Syrian involvement in various terrorist operations in Europe and diplomatic setbacks in neighboring Lebanon.

Yet despite shortages and long lines outside shops, outwardly Syria provides a unique example of a Third World country whose severe economic and financial problems have little discernible impact on government stability.

But, in part because of displeasure with Syria's alliance with non-Arab Iran, only Saudi Arabia among the Arab League member states still honors the pledge to contribute vital foreign exchange to Syria's defense budget, rumored to account for 40 percent of government expenditure.

Iran since September has stopped providing low-priced crude oil to Syria to signal that it is upset about more than $2 billion in unpaid oil bills.

Long buoyed by now greatly reduced remittances from Syrian workers overseas, the unofficial value of the Syrian pound has dropped by 50 percent in less than two years.

Some state enterprises in the socialist economy are shutting down for lack foreign exchange to buy essential spare parts and raw materials.

Western diplomats estimate annual inflation since the fall at roughly 70 percent, although seasonal variations in food prices account for much of the increase.

Daily power cuts of four hours in Damascus and elsewhere, officially blamed on drought rather than rapidly expanding rural electrification and subsidized rates, are expected to double with the onset of summer.

Aleppo, Syria's second city, is bracing for water shortages due to problems with six of the eight turbines at Assad Dam on the Euphrates River and because recent negotiations with Turkey to provide more water and power fell through.

Syria's outward tranquility is due in part to the no-nonsense nature of the government and, in part, to the public knowledge that the country's plight is shared by almost all its Arab neighbors.

Much of the current squeeze is due to the relatively straitened circumstances of the Arab oil producers of the gulf confronted with lower crude prices and cutbacks in their own once prosperous economies.

For more than a decade their seemingly uninterrupted gifts, loans and other largesse contributed mightily to the balance of payments of Syria and other poorer Arab countries which, also profited from the petrodollar bonanza by exporting workers to the gulf region.

Now, although there are no reliable, up-to-date statistics, remittances from Syrian workers abroad appear to be down, reflecting layoffs or lowered salaries for those still employed.

If Assad does improve relations with Iraq, informed sources suggested he may justify his decision on grounds of economic necessity while arguing that his Iranian alliance, and Syria's and Iran's mutual hatred of Iraqi President Saddam Hussein, remain firm.

Syria's rivalry with Iraq, which goes back to ancient times, is aggravated by the fact that Assad and Saddam Hussein are leaders of estranged wings of the pan-Arab nationalist Baath Party.

Were Syria to reopen the 500,000-barrel-a-day Iraq Petroleum Co. pipeline running across Syria to the the Mediterranean, which Assad ordered shut in 1982, more than mere transit rights and fees are likely to flow into the treasury, officials argued.

Kuwait and other gulf states could be expected to reward the breach in the Syrian-Iranian alliance by resuming lapsed subsidy payments first pledged at the 1978 Arab League summit in Baghdad. Saudi Arabia could be counted on to increase its estimated annual $560 million stipend, the officials added.

The officials also mentioned the "invisible domestic dividend" of ending the secular Syrian government's uneasy alliance with Iran's radical Shiite Moslem fundamentalists.

Whatever Iran's displeasure with any breach of its alliance with Syria, officials in Damascus argued that keeping the Assad government in power is crucial and that the Syrian economy has already "suffered enough."

Sources close to the Soviet Union noted that the Kremlin long has pleaded with Syria, its main Arab ally, to improve ties with Iraq.