Robert Mugabe, a mystery to much of the world when he became prime minister of newly independent Zimbabwe last year, has finally dropped some of the veils obscuring his enigmatic political style.

Ten months after his overwhelming election victory transformed him from a guerrilla leader into one of Africa's most important politicians, he demonstrated last weekend that he can exercise his authority with stunning effect.

Dominating a press conference in which he announced a major Cabinet shakeup, he showed he is not afraid of a high-stakes gamble once he has laid the groundwork. He also made it evident, with barely concealed humor, that he enjoys the Western concern over his professed Marxism.

Consider his actions at the Saturday press conference where Mugabe:

Demoted his long-time nationalist rival, Joshua Nkomo, by removing him from the ministry that controls the police. Nkomo has complained and so far refused to accept his transfer but there are numerous indications that he has little choice but to fall in line. Meanwhile, his successor has already moved into his office at the Ministry of Home Affairs.

Fired his main nemesis in his ruling party, Edgar Tekere, from his post as manpower minister. Tekere, who revels in his "tough guy" image and reputedly had strong backing within the military, has exited without a whimper -- at least so far.

Strongly defended his Marxist ideology. He then, however, proceeded to define his Marxism in terms of ending worker exploitation -- a philosphy that many capitalists could accept. "I don't think he'd pass an exam on Marxism if his professor was Soviet," a Western diplomat said.

Mugabe's gamble involves Nkomo, the 30-year veteran of Zimbabwean black natonalism who first was Mugabe's leader, then a coequal and is now his subordinate.

Mugabe has deftly sugarcoated a bitter pill for Nkomo by offering his Patriotic Front Party two more positions in the Cabinet but removing the party from involvement in security matters which are still far from stable after a seven-year guerrilla war.

Nkomo is faced with the choice of either accepting his lowered status as minister of public service or pulling the Patriotic Front out of the nominal government coalition and becoming an opposition party.

One of Nkomo's deputies noted wryly, "The history of opposition parties in Africa is not a cause for optimism."

The real danger of such a move is that it could lead to civil war between Mugabe's Shona-oriented party and Nkomo's organization which is dominated by the minority Ndebele tribe from the southwestern part of the country.

As a result of the war, both parties still have heavily armed military organizations with a combined total of about 30,000 troop.A civil war would be disastrous for the country, undermining the fledging efforts at rehabilitation from the war.

Mugabe's gamble on that score is probably safe.

"The Patriotic Front would never start or foment war or violence," a key Nkomo aide said, although he hedged, noting that ill-considered actions by the other side could bring it about.

There is always the possibility, however, that widespread violence between the two military organizations as occurred in Bulawayo two months ago could be sparked by sporadic incidents. Four persons were injured in a clash yesterday in Chitungwiza township outside Salisbury where about 10,000 former guerrillas from both sides are living while they await integration into the national Army.

Nkomo's problem is that he can win neither an election or a war.

Mugabe's carefully crafted moves have left Nkomo with a dilemma: If he swallows the pill it is one more step in the eventual demise of his party. Some of his military forces may decide to resist anyway and the result could break up the party. If he goes into opposition he could lose some of his key people who are tired of being in the political wilderness and want jobs in government.

In response, Nkomo has stalled, delaying a meeting of his 156-member central committee until the end of the week. Analysts interpret this to mean he is letting emotions cool, an indication that he will find a way to accept Mugage's offer, possibly after regaining some role in the area of security.

Because of opposition within Mugabe's party, Nkomo's demotion had been planned since shortly after he got the police job at independence last April, according to a source close to the prime minister.

Tekere's removal was also in the works for months although it came as a surprise to outsiders since just last month the outspoken minister was acquitted of murdering a white farmer, a verdict that seemed to enhance his popularity among Africans.

For months Mugabe had been undercutting the man who is still secretary general of his sometimes undisciplined party. There has been no sign of protest over his ouster, indicating that the controversial former minister's backing was mainly ephemeral.

Mugabe's main complaint with Tekere was simply that he did not do his job, according to a number of sources. Tekere was rarely in the office and did little to organize the ministry to handle the manpower needs of the nation.

The last straw for Mugabe, who follows a rigid work ethic, reportedly came shortly before Christmas when Tekere arrived 90 minutes late for a Cabinet meeting, insisted that an item concerning his ministry be taken up immediately even though it was low on the agenda and then walked out when he did not get his way.

Mugabe protected his flanks well from any possible radical backlash over ousting Tekere. In the last month he talked more about government participation in the economy and arranged the takeover of the South African-controlled press. He also promoted some radically inclined officials in the weekend Cabinet reshuffle.

His remarks on Marxism fit in this context also.

There is little question that Mugabe believes in a socialist economy with significant elements of government participation and control. Mugabe is a pragmatists, however, and realizes he has inherited a capitalist economy that is thriving by African standards and he is not about to dismantle it hastily.

In a political sense his Marxism is probably best defined as anti-captialism, since it was the capitalist system that fostered white exploitation of blacks in the country. Such Marxism cannot help but have an appeal in a country where the dichotomy between white and black standards of living is enormous.

So Mugabe can be expected to continue preaching his form of Marxism despite Western discomfort.

Yesterday a U.S. Congressional delegation told him that such statements could affect aid and investment. Mugabe just nodded.