Robert Mugabe's announcement of a broad-based coalition government to take office on the independence of Zimbabwe next month raises the question of where true power will lie in the new republic.

The incoming prime minister can look to three institutions through which to rule -- the 100-member Parliament, the newly appointed Cabinet of 23 ministers or the 28-member central committee of his Zimbabwe African National Union Party.

It is the potential power play between the last two groups that has aroused the most interest. Mugabe's party has been run by the central committee with an inner national executive body since the party held its first Congress in 1964.

The reformation of the party's inner circle in 1977 led to the expulsion of such rebels as Rugare Gumbo, then publicity secretary, and to the inclusion of Mugabe's wife Sally as deputy women's affairs secretary and a guerrilla commander's wife, Teurai Nhongo.

When Mugabe arrived in London last year for the peace conference he brought with him the backing of a group that was united in support of his leadership. There are, however, ethnic and tactical differences within the central committee.

Just as the need for national reconciliation compelled Mugabe to include two white ministers as well as Nkomo and three of his supporters in his Cabinet, the debt he owed to his own central committee for participation in the seven-year war against white control of Rhodesia had to be paid. Of the 23 Cabinet ministers, 14 are from the central committee.

There are still some exceptions, including Nathan Shamuyarira, a journalist who never joined the central committee since he participated in an independence movement based in Zambia called the Front for the Liberation of Zimbabwe. Mugabe obviously felt close to Shamuyarira and assigned him to the Information Ministry, even though other control committee members resented his rival struggle for independence.

It is this combination of political appointees and talented leaders that suggests Mugabe has been able to pay off past debts and plan for the future in structuring his Cabinet.

To a large extent the central committee and the Cabinet overlap. Although the overlap is considerable, the power of the secretive central committee is bound to diminish since many of its members will be forced to debate issues in the Cabinet and defend policies in the Parliament. fMugabe, who has been accused of weak leadership within the committee for bending to consensus and avoiding infighting, is now in a strong position to subject his more unruly aides to the wider range of opinion within the open forums of the government.

Mugabe's choice to head the Manpower Ministry, Edgar Tekere, is regarded by most observers as one of the more troublesome members of the central committee. As secretary general of the party he wields influence, but his erratic behavior and deep-seated animosity to Nkomo's party considerably embarrassed Mugabe during the London peace conference.

He remains a force, however, although the shift to a more open style of government may well diminish his authority. There is little doubt that Mugabe will reshuffle his Cabinet once he has begun to consolidate power and both the awkward or incompetent ministers with senior party positions may well find themselves destined for remote diplomatic posts.