The strife-torn colony of Rhodesia became the independent, black-ruled nation of Zimbabwe today, ending 90 years of white domination and 15 years of illegal independence.

Prime Minister Robert Mugabe took the oath of office shortly after mid-night in a ceremony at Salisbury's main stadium while representatives of about 100 countries and about 35,000 cheering Zimbabweans watched.

Mugabe, the guerrilla leader most feared by the white-minority community before his election last month, made an eloquent plea to the people of Zimbabwe to end the hatered of seven years of war.

"The wrongs of the past must now stand forgiven and forgotten," the new prime minister said in a speech he wrote. "If yesterday I fought you as an enemy, today you have become a friend and ally with the same national interest, loyalty, rights and duties as myself.

"If yesterday you hated me, today you cannot avoid the love that binds you to me and me to you."

The independence ceremony, presided over by Prince Charles, heir to the British throne, began at midnight when the Union Jack was lowered for the last time in an African colony and the new five-colored Zimbabwe flag was raised.

The lowering formally ended the 128-day "second British empire" in Africa that began when the temporary British governor, arrived here Dec. 12 to oversee the transition from the white-dominated government and the elections that brought Mugabe to power. The transistion followed a British-sponsored peace conference last fall.

The crowd, all there by invitation, was subdued for most of the British-oriented ceremony but it came alive and roared approval as a 21-gun salute accompanied the raising of the new flag. a

Police set off tear gas bombs outside the stadium in the black township of Harare to disperse crowds. In general, however, the celebrants were cheerful but orderly.

Prince Charles drew cheers from the crowd when he used the Shona word for independence in a speech echoing Mugabe's theme of reconciliation. British Foreign Secretary Lord Carrington read a message from Prime Minister Margaret Thatcher in which she pledged close cooperation in helping in reconstruction and development of the country, a theme Mugabe noted with satisfaction.

Among the witnesses were Indian Prime Minister Indira Gandhi. Pakistani President Mohammed Zia ulHaq, Austrailian Prime Minister Malcolm Fraser and several African presidents. U.N. Secretary General Kurt Waldheim also attended.

Mugabe's rival guerrilla leader, Joshua Nkomo, appeared to be near tears as the flag went up.

Missing from ceremonies was former prime minister Ian Smith, whose 1965 declaration of independence from Britain to preserve white-minority rule started the crisis that eventually led to the bloody guerrilla war. He is on a lecture tour of South Africa.

For black Africa, Zimbabwe's independence represents a high-water mark in the effort to achieve majority rule on the contintent.

"Now only the big apple, South Africa, is left" along with its illegally controlled territory of Namibia (Southwest Africa), one Zimbabwean said.

Mugabe's main problem is to bind the emotional wounds of a war that killed at least 30,000 people and to rebuild the countryside where hundreds of schools, clinics and hospitals were destroyed and more than a million people were left homeless.

Mugabe, who has downplayed his Marxist leanings while seeking to build bridges to the West since his election, noted that the country's great need for outside assistance.

"We have certainly won the good will of many countries and can confidently expect to benefit from the economic and technical aid they are able and willing to provide for us," he said.

Although reassuring the 200,000 white population there will be no retaliation for past injustices, he said the government is determined to bring about "meaningful change to the lives of the majority of the people."

He cautioned blacks, however, not to expect immediate changes.

"I must ask you to be patient and allow my government time to organize the programs that will effectively yield that change," he said.

Bishop Abel Muzorewa, who proceeded Mugabe as prime minister and was the first black leader in Rhodesia, rapidly lost popularlity as little changed in the lives of the 7 million blacks since his government was still controlled by the white minority. The euphoria of this weekend's independence celebrations could quickly be forgotten if Mugabe does not move rapidly in some areas.

He has some major advantage over Muzorewa, however,

The country no longer has to prosecute a war that was costing about $1.5 million a day. The internationally approved settlement negotiated by the British brought an end to international economic sanctions and has assured recognition and the promise of assistance from many countries.

Britain already has promised $165 million in assistance and the United States has pledged $20 million this year with another $25 million next year pending congressional approval.

One of the key issues of the war was hunger for land since half of the country's land is controlled by about 5,000 white farmers. Mugabe has pledged not to expropriate white-owned farms but has said the government will seek to settle black farmers on vast areas of land that are unoccupied because of the war.

In a press conference yesterday he said key priorities of his government would be to speed up integration of the three armies that are a remnant of seven years of war, reselttlement of displaced persons and restoration of schools and hospitals.

Integration of the military is an especially senstive problem that will have to be tackled urgently. A tentative start has been made in formation of one Army for Zimbabwe.

Rhodesian military forces that served Smith's and Muzorewa's governments are training under British supervision forces. Along with them are about 1,300 guerrillas, but more than 32,000 others are still in assembly points established by a monitoring force of Commonwealth troops during the cease-fire and now run by the military Mugabe has inherited from the Muzorewa government.

The new prime minister said at his press conference that the integration has to be speeded up and the assembly points closed.

Mugabe has appointed Lt. Gen. Peter Walls, who led the long fight against the guerrillas, to head a joint high command from the Army, Air Force and Mugabe's and Nkomo's guerrilla forces.

Another potential problem is the possibility of friction in the Mugabe-Nkomo alliance, which is divided along tribal lines.

Nkomo's Patriotic Front has been grumbling about receiving only four of the 23 Cabinet seats, with the only significant one being Nkomo's Home Affairs Ministry. Mugabe controlled the appointment of half the 40 Senate seats and all but one went to his own party.

In the February parliamentary election, Mugabe's party won 57 of the 80 seats in the lower house with the Front getting 20 and Muzorewa's party three. The other 20 seats are reserved for the whites and were all won by Smith's Rhodesia Front Party.

The election was the culmination of a process that began in August at the Commonwealth summit in Lusaska, Zambia, when Britian agreed to make a new effort to achieve a peaceful solution to the seemingly interminable Rhodesian problem.

Thatcher's govenment inherited a novel situation after eight major attempts to bring about legal independence had failed. All sides seemed to have reached a point of exhaustion with no prospects of any end to the escalating war.

Carrington deftly worked his way through a stage-by-stage conference that started Sept. 10.

Agreement was first reached on a constitution, then on the transitional government run by Britain and finally on a cease-fire. The conference took 15 weeks and the overall agreement was signed Dec. 21.

When the temporary British governor, Lord Soames, was preparing for the elections the colonial government accused Mugabe's forces of the most serious violations of the cease-fire, and Mugabe and Soames exchanged bitter words.

Since the election, however, all has been sweetness and light. In a farewell address Monday, Soames spoke of his "admiration and respect" for Mugabe.

Mugabe responded in kind in his speech tonight calling Soames "a great man" who performed "a difficult and most unenviable task" with "remarkable ability and overwhelming dignity."

"I must admit that I was one of those who originally never trusted him, and yet I have now ended up not only implicitly trusting but fondly loving him as well," the prime minister said.