The United States plans to land Marines from amphibious assault ships at Oman and Somalia and drop 82nd Airborne paratroopers over western Egypt next month in the most dramatic demonstration to date of America's ability to aid its friends in the region, officials said yesterday.

To underscore the emerging alliance, and as a reaction to pressures from Libya, the plan calls for Egyptian and, tentatively, Sudanese troops to join the maneuvers in Egypt's western desert abutting Libya.

The exercise, called "Bright Star," would be much larger than last year's 10-day exercise around Cairo, which involved only U.S. and Egyptian troops. This one is tentatively expected to last from Nov. 9 to Dec. 6 and involve U.S. ground, air and naval forces in exercises over thousands of miles.

"The idea is to assure countries over there that we could come to their aid in a hurry," said one official, acknowledging that fears about Libya's stepping up military activity in Chad and Sudan added a sense of urgency to this second "Bright Star" exercise.

Even though Israel figures in the U.S. "strategic" grand design for the area, it will not be involved in "Bright Star," possibly because of the sensitivities of Islamic allies of the United States.

Less than a week before he was assassinated, Egyptian President Anwar Sadat dispatched his vice president, Hosni Mubarak, here to request a strong U.S. reaction to the growing Libyan activities in the area, with Sudan the primary worry.

Although planning for "Bright Star" was well along when Mubarak arrived, officials said that the exercise was expanded in response to the Egyptian plea and the killing of Sadat.

Fast-moving events in the Middle East and Africa may cause some parts of the "Bright Star" plan to be changed, including the timetable.

Administration officials said the exercise will show the power of the United States and its regional allies to counter the Libyan-Ethiopian-South Yemeni pact signed in Aden Aug. 20. This alliance of radical states, sponsored by Libya's Col. Muammar Qaddafi, generated fears elsewhere in the region and in Reagan administration councils.

Marines already afloat in the Indian Ocean will, under the new "Bright Star" plan, go ashore on Oman's island of Masirah while others will land at the Somalian port of Berbera. In an attempt to show the breadth of the alliance, Omani and Somali forces would support the Marines coming into their ports.

On the ground, plans call primarily for an American and Egyptian show of striking power, with Sudanese in supporting roles. In the air, B52 bombers will fly from North Dakota to Egypt, drop bombs on test ranges and return nonstop to the United States.

The combined military maneuvers are to take place in a troubled and strategic area that increasingly resembles a checkerboard of radical and conservative states with conflicting alignments to Moscow and Washington, respectively.

Each superpower and its leading regional partners insist that their moves are essentially in reaction to the other. The regional dimension of the struggle is deepened and complicated by longstanding and even ancient enmities.

The tripartite alliance of Libya, Ethiopia and South Yemen engineered by Qaddafi two months ago, according to the treaty text, is in response to "the coordinated conspiracies of international imperialism, Zionism, racism and reactionary forces to encircle, strangle and reverse the revolutions of their three countries."

At the moment Qaddafi was in Aden to complete the treaty, U.S. warplanes of the Sixth Fleet shot down two challenging Libyan fighters in the Gulf of Sidra, further heightening the Libyan's anxiety.

Reports reaching Washington initially said Qaddafi offered to supply $900 million in aid to his two treaty partners. Subsequently, the figure was reduced to $100 million, which may be a first installment.

Libya has been encountering cash-flow difficulties due to sluggish oil sales and prices, and U.S. intelligence does not believe that any of the cash actually has been supplied, officials said.

Moscow's role in encouraging or generating the pact is unclear, according to Washington officials. Soviet and other communist bloc forces and advisers are in all three countries. Whether or not Soviet military men were involved, Washington received many reports that joint military planning of the three partners is under way.

This aspect of the pact greatly alarmed Sadat and Sudanese President Jaafar Nimeri. The Sudan, already embroiled with Libya over the mini-war in Chad on its west, feared the prospect of Libyan-backed trouble on its other flank, from its eastern neighbor, Ethiopia. The Sudan's security, in turn, is vital to Egypt.

Further east, Somalia and Oman were gravely concerned about Qaddafi's new connection with their respective neighbor-enemies, Ethiopia and South Yemen. Both Somalia and Oman signed up with the United States last year to provide facilities to U.S. emergency forces.

Moreover, the Persian Gulf's big chip, Saudi Arabia, while steering clear of formal military alliances or pledges of combat cooperation with the United States, was also disturbed by the evidence of Libyan activism and the three-way alliance.

The U.S. military exercise to reassure its partners with proof of American power and determination is considered certain to draw strident verbal responses from Libya, its treaty partners and the Soviet Union. Whether the reply will encompass more than angry words is unknown.

At the White House yesterday, President Reagan said a speed-up in military assistance to Egypt and Sudan is "called for."

Asked whether U.S. troops would see combat in Sudan, Reagan said:

"We have no intention of any Americans engaging in combat."