The doctrinaire leader of South Yemen, Abdul Fattah Ismail, resigned today as Socialist Party secretary and president of the Arab world's only Marxist state. He was replaced by his prime minister, Ali Nasser Mohammed.

The unexpected leadership change, announced by the official Aden Radio, could have important repercussions in the struggle between the United States and the Soviet Union for influence and strategic advantage on the foot of the Arabian Peninsula with its petroleum treasures and proximity to the Islamic turbulance of Iran.

There was speculation that Ismail fell from power maily because of recent indications that he was considering drawing closer to Saudi Arabia, the peninsula's dominant power but a firm opponent of the Marxism espoused by the South Yemeni leadership. His foreign minister recently visited Saudi Arabia and Ismail was scheduled to make a trip there soon.

Ismail's successor, Mohammed, has been a consistent advocate of close ties with the Soviet Union. At the same time, however, he is known as a skilled administrator and an economic pragmatist, leading observers to predict he could turn out to be less of a faithful Marxist in his dealings with the Soviet Union and more interested in promoting South Yemen's own national interests.

The apparent political demise of Ismail was viewed with particular interest because it came as the United States seems headed for a showdown with Iran that could include a blockade of the Persian Gulf on the other side of the peninusula. Soviets reconnaissance planes and ships use South Yemeni facilities at Khoromaksar and Al Mukalla on the Gulf of Aden to monitor U.S. ships in the Indian Ocean and Persian Gulf area.

It is South Yemen's location -- dominating the narrow Bab al-Mandeb passage between the Indian Ocean and the Red Sea -- that gives the country its strategic value. It has no petroleum of its own to speak of and only .2 percent of its 112,000 square miles are under cultivation.

Ismail, a 41-year-old former oil refinery laborer, made the Soviet Union the exclusive beneficiary of this location after he took power in July 1978 and had himself named president of the Presidium of the Supreme People's Council. Last year he signed a 20-year treaty of friendship and cooperation with Moscow. Nearly 1,000 Soviet advisers helped him run the country, along with about 700 Cubans and a number of East Germans officering internal security troops.

Although considered less dogmatic than Ismail, Mohammed's history of favoring South Yemen's close relations with the Soviet Union made unlikely any radical or immediate changes in the strong Soviet military presence accepted by Aden.

The radio announcement said Ismail resigned because poor health prevented him from carrying out his duties, without specifying his malady. This was interpreted by analysts in Cairo and Beirut as a euphemism designed to put the best face on what they said was the outcome of a battle for power within the secretive Aden leadership.

Although he resigned both as chairman of the presidential council and party secretary general, the announcement said he was named to the position of party president. This was viewed as an honorary post, however, safely removed from the levers of command in the Presidium of the Supreme People's Council.

Journalists who covered Ismail at last week's Steadfastness and Confrontation Front summit conference in Libya said he showed no signs of ill health during late-night negotiating sessions there.

Mohammed, 40, is a former primary school headmaster. He worked with Ismail for years in the National Liberation Front that fought to drive the British from what was until 1967 a backwater colony that had been important as a stopoff for steamers moving east from the Suez Canal in earlier days.

The United States has had no relations with South Yemen since 1969 and there is no U.S. Embassy there. Information about what goes on in Aden is accumulated mostly through satellite.

The tone of relations with North Yemen, and by extension with Saudi Arabia, is regarded as a key indicator of the course Mohammed will set for his government.

Ismail came to power in street battles precipitated by disagreement over then-president Salem Rubai Ali's willingess to deal with Saudi Arabia and the United States with an eye to liberalizing the socialized economy and benefiting from Saudi oil wealth. Analysts speculate that Ismail now has fallen as a result of willingness to improve relations with the Saudis.

Observers in Cairo pointed out, however, that Mohammed's own position on the recent signs of improved relations with the Saudi Arabia was not known. On one hand, he was the victim of an assassination attempt in March 1972 said to have been carried out by South Yemin dissidents backed by Saudi Arabia. On the other, his economic pragmatism has led him to seek an end to Aden's isolation and he took part in negotiations that led to diplomatic relations with Saudi Arabia in 1976.

North and South Yemen often talk of unity -- they formally agreed to it in 1972 -- but their leaders and systems have been hostile for years. Frequent tribal skirmishes mark their rugged border stretching from Bab al-Mandab the Saudi border and North Yemeni charges of an invasion from the south led President Carter to send an emergency arms shipment to Sanaa in March 1979.

Since then, however, North Yemen has quarreled with Saudi Arabia and resumed accepting aid from the Soviet Union. In addition, an opposition group supported by South Yemen recently announced agreement with the Sanaa leadership on participation in the government, leading to predictions of improved relations between north and south at the expense of Saudi Arabia's dominant influence in Sanaa.

The warming atmosphere between north and south reportedly was chilled by Saudi Arabia in recent weeks through agile use of aid payments to those parts of the North Yemeni government favorable to Riyadh. The outcome of that struggle remains to be seen, however, and Mohammed's ascent to power in Aden is likely to play a preponderant role in it.