Chester Crocker, assistant secretary of state for African affairs, will head one of two western delegations that will be in Angola and South Africa on Thursday and Friday in an attempt to make progress in the negotiations on Namibian independence.

The State Department announced yesterday that Crocker and Jean Ausseil of France will lead the delegation going to Luanda for talks with Angolan leaders and Sam Nujoma, president of the Southwest Africa People's Organization, which has waged guerrilla warfare against South Africa's control of Namibia.

The Western Contact Group, composed of the United States, France, Britain, West Germany and Canada, has been mediating among the contesting factions in Namibia, South Africa and the so-called "front-line states" of black Africa in hopes of working out a plan leading to independence for the mineral-rich territory on South Africa's northwestern border.

The State Department said the purpose of the new missions is to bring to a close the first phase of the negotiations and to obtain agreement from all the interested parties "that the time is ripe to move ahead to phase two discussions."

The first phase of the negotiating timetable set by the contact group has involved provisions for electing a government in Namibia. Although South Africa has agreed to the proposed proportional-representation voting plan, SWAPO has objected, and the department announcement said the delegations will set forth some new ideas for overcoming these objections and allowing a conclusion of phase one.

The second phase is scheduled to deal with implementation of the voting under United Nations supervision. The department said the delegations also will be carrying a new proposal aimed at obtaining agreement by SWAPO and the front-line states to the constitutional principles that the western five have proposed for Namibia.