The Zimbabwe-Rhodesia peace conference took a major step forward today when all sides agreed to a British-run interim government leading to new elections and legal independence under black-majority rule.

The agreement on the transition completed the second stage of the talks here aimed at resolving the 14-year-old racial conflict in the southern African breakaway colony. The third stage -- negotiation of a cease-fire to end the guerrilla war -- remains.

A final settlement of the conflict, which began when former prime minister Ian Smith illegally declared independence from Britain to maintain white-minority rule, is now expected within a week or two.

Night-long contacts between British and Patriotic Front guerrilla delegates at the peace talks preceded today's agreement to the British transition plan, which the white-backed Zimbabwe-Rhodesian government of Prime Minister Abel Muzorewa had accepted two weeks ago.

No one today underestimated the problems to be surmounted in negotiating a cease-fire. But there was wide spread belief that the three delegations have come too far to fail, having agreed on an independence constitution and the transitional plan.

The political problems now have been settled, leaving only military questions. The cease-fire negotiations that start Friday will involve military officials from all sides, and British sources noted that the more direct approach of the military men may lead to more rapid progress.

British Foreign Secretary Lord Carrington, chairman of the conference, praised both the Zimbabwe-Rhodesian government and the Patriotic Front guerrillas for their "wisdom and statemanship" in reaching today's agreement.

[In Washington White House Press Secretary Jody Powell said the British government deserved "tremendous credit" for what had been accomplished in the London talks.]

The spokesman for Front leaders Joshua Nkomo and Robert Musabe, Eddison Zvobgo, said that "history is being made. I can confidently say that a new dawn, a new hope will shine on our people."

Muzorewa's spokesman, David Zamuchiya, said the Salisbury government was "happy that the Patriotic Front finally accepted."

Muzorewa refused to attend the conference after accepting the British proposals two weeks ago. Since then he has stayed in the backgrounds while Britain and the Front worked out their differences.

Today's agreement came 14 years to the day after Britain imposed economic sanctions on its rebellious colony. The British government allowed the sanctions order to lapse today on the basis that a settlement was near, although sanctions against direct trade with Zimbabwe-Rhodesia remain in effect through other laws.

On the surface, today's agreement resulted from simple insertion of one sentence into the British transition plan presented earlier this month. British agreed that the Patriotic Front forces as well as the Salisbury government's military forces should come under the authority of the British governor during the transition.

The Patriotic Front interprets this to mean that its troops have been granted legal status in recognition of their role in bringing about a peace settlement. Britain did not disagree with that interpretation.

It may seem surprising that such an interpretation could be crucial to a settlement that has eluded four British governments in eight previous attempts -- while the war in Rhodesia killed more than 20,000 people. To the Patriotic Front, however, the sentence means that its forces have been granted legitimacy and equal status with those of the Salisbury government, an important issue in the election to be fought next year.

Today's agreement, and private understandings worked out this week, provide that:

The Muzorewa government will step down and Britain will assume authority during a two-month transition period and the election of the new black-majority government.

The existing Rhodesian police force will be responsible for law and order during the transition, supervised by a special contingent of British police.

The election will be supervised by a council chaired by a British official with participation by all parties.

The election will be observed by representatives of the British Commonwealth parties, who also will provide troops to monitor the cease-fire.

The cease-fire will be supervised by a commission of military men from Britain and the two opposing sides.

Arrangements will be made for Patriotic Front forces in Rhodesia to be housed and fed, an inducement for them to abide by the cease-fire. In addition Britain and other countries, including the United States, will help resettle the hundreds of thousands of Rhodesian refugees now in neighboring countries.

The date and details of the cease-fire are still to be negotiated.

[Mugabe in a messege from London to his forces in Mozambique ordered them to step up operations against the Salisbury regime, Agence France-Press reported today from Maputo. This was thought to be an effort to get the maximum number of his guerrillas into Rhodesia prior to cease-fire terms being negotiated.]

Although there is widespread confidence that the London conference will end in overall agreement, there is considerable concern that Britain will have difficulty enforcing a cease-fire in a country that has become an armed camp over the last decade.

Meanwhile, it was revealed today that Britain came under some last minute pressure to reach agreement. Oil-rich Nigeria sent Al Haji Maitama Sule, a special representative of President Shehu Shagara, to meet with British Prime Minister Margaret Thatcher yesterday.

His message, diplomatic sources said, was that Nigeria believed the only acceptable settlement was one involving all parties.