DAMASCUS, Syria (AP) _ A string of oil discoveries in the eastern desert and a new determination to encourage private business are helping socialist Syria climb out of a deep economic trough.

With the help of Western oil companies, the country this year became a net oil exporter for the first time, with revenues of $550 million forecast by early 1990.

''Self-sufficiency in energy is something you really appreciate when you've never had it before,'' Economy Minister Mohammed Imadi said in an interview.

''The studies show that we have a continuous oil and gas supply for our needs and a surplus for export whenever we need the foreign exchange,'' he said.

For the Syrians, whose economy has been in such poor shape it barely had enough foreign exchange to cover one week's imports, the oil flow offers the prospect of badly needed money.

The modest oil boom has come as Syria struggles to reduce annual inflation of more than 65 percent and repay its $18 billion foreign debt.

Three-quarters of that is owed to the Soviet Union, mostly for arms supplies for President Hafez Assad's determination to make Syria strategically equal to neighboring enemy Israel.

The oil strikes have come at a critical time for Syria, which has suffered political setbacks in the region and is under pressure from the Arabs and the Soviets to moderate hardline policies hindering the Middle East peace process.

Saudi Arabia this year stopped annual payments to Syria of around $540 million for its role as a frontline Arab state facing Israel.

Other Arab states have long halted aid to Syria, mainly because of Assad's alliance with Persian Iran against Arab Iraq in the 8-year gulf war.

Oil giants Royal Dutch Shell, British Petroleum, Occidental Petroleum of the United States, and France's Total are among 10 foreign companies involved in exploring and developing the new fields as quickly as possible.

''It's a high-pressure job because the Syrians are really in a rush to get the oil out of the ground,'' said one exploration expert, who spoke on condition of anonymity. ''The better we do, the more we're asked to do.''

Syria has been pumping around 150,000 barrels a day of heavy crude from the Souweidieh fields in the northeast since the early 1970s and mixing it with imported light crude for domestic use.

Prospecting at that time by the country's East bloc allies brought no results, but advanced technology helped Shell locate the Thayyem fields in 1984.

The new wells already are producing around 200,000 barrels a day of saleable crude, raising overall output to 350,000 barrels a day, more than double the country's needs.

But because the deposits are ''generally small and fractured, exploration will have to be continuous in order to guarantee long-term supplies,'' the expert said.

Oil Minister Mutanious Habib recently told the Middle East Economic Survey, an oil industry newsletter, that another 50,000 barrels a day will be added later this year from three new fields.

He said Syria was evaluating potential reserves throughout the country in what he called a crucial year for exploration.

The government also has signed a contract with Marathon Oil of the United States to develop natural gas deposits south of ancient Palmyra, to be used instead of oil and hydro-power for generating electricity.

Imadi said the increased oil output and a record harvest following higher- than-average rainfall helped the economy grow by a staggering 10.7 percent last year.

This year, agricultural production will fall sharply because of a winter drought that is already causing water shortages in Damascus. But officials estimate that the oil boom will still fuel growth of around 7.2 percent a year.

Syria is negotiating barter deals to settle accounts with foreign creditors and cut import bills. Phosphate exports, for example, will pay for importing antibiotics from France and Italy.

A senior government official said that a crackdown on smuggling is working, but that incentives for private businessmen are more effective for curbing the black economy.

Contraband ranging from bananas and French cheeses to clothing and computer software arrives in Syria by the truckload from neighboring Lebanon, foreign residents of Damascus say.

Under the new incentives, businessmen can use up to 75 percent of their export earnings to finance imports. They can also go into partnership with the government in tourism, transportation and agricultural business projects.

To attract expatriate Syrians to invest at home, tax incentives and a law allowing businessmen to transfer earnings abroad are being prepared. There are plans, too, for reviving the Damascus stock market after a quarter-century gap.

''It's common sense to have the private sector more actively involved in the economy,'' Imadi said.

But Western diplomats predict it will be a while before the Syrian economy takes off.

''There's a great commercial tradition here, but because of the complex bureaucracy, and corruption, it can't be revived from one day to the next,'' one commented.

Syrians say they find it hard to manage on salaries that range from about $63 a month for a taxi driver to $125 for a university professor.

The government recently hiked wages by 25 percent, but that only seemed to intensify the inflation problem. Gasoline prices immediately jumped by 50 percent and some food costs rose by 30 percent.