The Zimbabwe-Rhodesia settlement talks, now in their eighth week here, have reached a critical stage, with the Patriotic Front guerrillas under increasing pressure to agree to participate in British-supervised elections leading to black majority rule and legal independence for the country.

The current Salisbury government of Prime Minister Abel Muzorewa, backed by the country's white minority, has already agreed to the British plan, even though it would have to turn over power to a British governor during the election and transition period.

But the Patriotic Front guerrillas strongly object to Britain's intention that its governor administer the election essentially through the existing civil service in Salisbury and maintain law and order during the transition with the existing police force.

Patriotic Front leaders say this would enable the Muzorewa government and its white-dominated civil service and security forces to rig the election against the guerrillas, against whom they have been fighting a bloody war that has claimed an estimated 20,000 lives. If the Patriotic Front still, somehow managed to win the election, its leaders suggest, the security forces would be in a position to stage a coup and take back power.

The Patriotic Front wants the elections to be administered and the transition period policed by an impartial outside force like the United Nations or by a transitional authority in which the forces of the Muzorewa government and the Patriotic Front would share power.

Lord Carrington, the British foreign secretary and chairman of the Zimbabwe-Rhodesia conference here, has ruled out both these proposals. The British and the Muzorewa government fear that under either of these arrangements the Patriotic Front might seize power or control of the elections.

Carrington has insisted that the British will ensure that the elections are fair and that all parties will be free to contest them. The British plan to send several hundred of their civil servants from London to assist the transitional governor.

Britian also plans to have an election commission, made up of representatives of all the parties, advise the governor on election procedures and make complaints if necessary, Britain also has asked the Commnwealth nations, which include many of Zimbabwe-Rhodesia's black African neighbors, to send observers to check on the conduct of the elections.

The British have put off until the next and final stage of the talks here the question of how a cease-fire would be reached between the Patriotic Front and Salisbury government forces. The Patriotic Front wants the opposing armies intergrated during the transition, a change from its previous position that is should take sole control of the country's military. But the British want the forces to be frozen in place under the authority of the British governor.

"The fundamental question before you," Carrington told Patriotic Front leaders Robert Mugabe and Joshua Nkomo at today's negotiating sessions, "is whether you are willing to put your political support to the test under British authority."

"You are asking us to trust your governor on your word alone," Mugabe later answered, "despite the presence of the [Salisbury government's] police force and army."

"There must be trust on both sides," Carrington said. "In the absence of trust, no settlement can work."

Several possibilities for satisfying some of the Patriotic Front's doubts emerged today behind the scenes, where all deadlocks ultimately have been broken so far during the nearly two months of up-and-down negotiations here.

The British have made clear their willingness to take special steps to protect Mugabe, Nkomo and other Patriotic Front leaders and candidates from harm during the election campaign, This offer may include, according to knowledgeable sources, the British Special Branch security men who have been guarding the Patriotic Front leaders here.

The British also are open, according to sources to the possibility of expanding the number and role of the Commonwealth observers to satisfy the Patriotic Front that the elections were being conducted fairly and the transition policed properly. At a special meeting here today, the Commonwealth high commissioners told British officials of their willingness to assume a larger role although no specific plans were decided on.

Britain's decision to make the ninth major attempt in 14 years to negotiate a Rhodesian settlement was made possible by Prime Minister Margaret Thatcher's decision, under urging from Carrington, to drop her insistence that Britain simply recognize the biracial Muzorewa government and immediately lift the economic sanctions against it.

Under Thatcher's close supervision Carrington has been pushing to reach agreement on a settlement before the Nov. 15 deadline for renewal of the economic sanctions by Parliament. That also is the date Congress set for President Carter to drop similar U.S. economic sanctions against Zimbabwe-Rhodesia or explain why not to Congress, which could then overrule him by majority vote.

Thatcher remains eager to lift sanctions as soon as the British governor can be installed in Salisbury to supervise the transition to independence. She wants to put the Rhodesian problem behind her government which has devoted a vast amount of time and engery to it.

The real negotiations here have been the debates between Carrington's Foreign Office and Thatcher over how at each stage of the talks Britain should resolve the great differences between the Salisbury government and the Patriotic Front.

Once he has sold Thatcher on each British proposal, Carrington has presented it to the two sides on a take-it-or-leave-it basis. That was the only way, the British decided, they could force an agreement out of these talks after so many previous attempts had failed.