Secretary of State Cyrus Vance and British Foreign Secretary David Owen were presented with stiff demands last night by the guerrilla Patriotic Front on the Anglo-American plan to bring black majority rule to Rhodesia.

Political chiefs of the guerrilla alliance, Joshua Nkomo and Robert Mugabe, opened two days of negotiations with what an American source described as "hard positions - their maximum positions." He added, however, that "even in their maximum positions there is hope."

The American delegation had come here forecasting "agreement in principle," but the gap between principle and the specifics was strikingly evident last night. A British spokesman said, "It must be remembered that these are the gut issues, who shall hold power in Rhodesia."

Vance and Owen need enough agreement here to attempt to bring the Patriotic Front into a conference with the interim government set up in Rhodesia on March 3, composed of white Prime Minister Ian Smith and three moderate black leaders.

Last week, Smith and his black colleagues spurned an American-British call for all-party talks on Rhodesia, saying that they are determined to proceed with their plan for moving to black majority rule by Dec. 31.

The Patriotic Front, which has denounced the so-called internal settlement as a sell-out by black "puppets," indicated yesterday, as anticipated, that it will accept a joint conference. The Front is determined, however, to pin down the United States and Britain to conditions that will assure that Smith and his black partners will face terms that will sweep them out of power.

Last night Vance would say only that "they are serious negotiations" and "I don't want to characterize it any further." Owen said these talks may have to extended beyond their scheduled conclusion tonight.

The immediate issue here is not the potential conference between the internal and the external forces vying for control of Rhodesia. The most obstinate questions are the terms in the Anglo-American plan for a transition period of moving toward elections in Rhodesia.

Specifically, the issues are the temporary restoration of British authority in its former British colony, and the powers of a proposed United Nations peacekeeping force. The guerrilla leaders are suspicious that the Anglo-American plan will make unwarranted concessions to the 263,000 whites who dominate Rhodesia's 6.7 million blacks.

Beyond these issues, Vance and Owen told a closed meeting of the patriotic Front and officials of African nation supporting it that in a conference with Smith and his colleagues each side could bring up whatever it wished. Participants said no opposition was expressed inside the meeting but the Patriotic Front leaders took a sterner position in their public remarks.

There cannot be "a conference which seeks to marry us . . . with the so-called internal settlement," said Mugabe. Any conference, he said, must be on the basis of the Anglo-American plan, ignoring the "iniquitous agreement" between Smith and "the stooges."

In discussions with U.S. officials last month, Nkomo and Mugabi refused to discuss even the possibility of a conference with Smith and what they called "the puppet leaders" who negotiated a settlement with him.

Their change of position has occurred under the prodding of the neighboring nations, led by Tanzanian president Julius K. Nyerere, which have supported their guerilla war. These "front-line states" gave produced some flexibility on the part of the Front.

In Salisbury, however, the reverse has occurred, a hardening position by Smith and his new colleagues Bishop Abel Muzorewa, the Rev. Ndabaningi Sithoe and Chief Jeremiah Chirau. Last week these four internal leaders rejected calls for an all-party conference but agreed to meet with Vance and Owen.

The Vance-Owen objective right now is to get the patriotic Front leaders fully committed to the Anglo-American plan before going to Salisbury Monday to probe for bargaining room with Smith and the black leaders there.

Participants in the talks here include foreign ministers or deputies of the front line states - Tanzania, Zambia, Mozambique, Botswana, and Angola - and Nigeria.

The guerrilla chiefs have no intention "to accept anything that Smith proposes," a conference participant said. Nyerere, in a meeting yesterday morning with Vance with whom he had established very good rapport. Expressed sympathy with the ultimate fate of Bishop Muzorewa, it was learned. He is said to have told Vance, "we have to find a way to save the bishop."

Britain's Owen told reporters on his arrival that he believes Smith and his black partners eventually will negotiate with the Patriotic Front. "I think until they realize that their route does not offer them peace they will have a certain reluctance. But I am not totally pessimistic."