In an ordinary week in the new nation of Zimbabwe there is a grisly cast to the news.

A black child, innocent of danger, finds an abandoned grenade in a rubbish heap. He is blown to bits along with a 10-year-old playmate.

An elderly white farmer and his wife are murdered at dawn by two black strangers carrying AK47 rifles.

A gang of drunken whites attacks an interracial group at a Salisbury nightclub, beating one man senseless, breaking another's jaw.

Two men, a woman and an infant are cut down by AK47 fire in a beerhall robbery and then bayoneted to death.

There has been a larger bloodletting, too. A few weeks ago at Entumbane in the Western Province, white-led government troops slaughtered nearly 300 former guerrillas who had staged a mutiny.

Incidents of this kind create an impression of instability or near anarchy in the aftermath of a seven-year ago, black majority rule to the old colony of Rhodesia. That impression is over-drawn.

Compared to the grim expectations of 18 months ago, a remarkable peace has been achieved. The violence recorded since Prime Minister Robert Mugabe took power has been on a level with, say, the violence in Texas in 1980.

On my last trip here, in November 1979, there was awful foreboding in the white community and among many of the black middle class. There were predictions of a full-scale civil war between the tribal forces of the two guerrilla leaders, Mugabe and Joshua Nkomo. An alternative outcome was a military coup by the white-led Rhodesian security forces. A third scenario was South African intervention against a Marxist black government aligned with the Soviet Union and Cuba.

Nothing of the sort has occurred, even though the countryside is alive with armed men -- tens of thousands of former guerrillas and thousands of white former soldiers. There are moments of uneasiness and tension but the anticipated bloodbath has not happened; the prospects for that outcome now seem remote.

In large part this is the result of the conciliatory policies pursued by Mugabe and his government. He has been generous and sympathetic toward his erstwhile enemies, the white minority. He has sought, with fair success, a truce with Nkomo and his followers. He has maintained economic relations with South Africa and has rejected a Soviet-Cuban embrace.

The military task confronting Mugabe last year was to integrate into the national Army the 35,000 or so guerrillas who has taken part in the liberation war. As they came in to assembly points, they would turn in their weapons and be assigned to training battalions. If found unsuitable for professional military life, they would be wedded out and returned -- unarmed -- to civilian pursuits.

It was a sensible solution, but it has been difficult to execute. A major problem, as a Mugabe adviser put it, is that "the political results of last year did not reflect the military realities." Mugabe is a member of the Shona tribes, which make up 80 percent of the population. He won an overwhelming victory in elections against Nkomo, who comes from the minority Ndebele tribe. But the two men commanded armies of approximately equal size, armies that had clashed from time to time even as the war proceeded. The immediate post-election question was whether Nkomo's troops would accept the result. Some have not.

There have been a number of incidents over the past year, most arising out of the military integration process. As men from the two guerrilla armies came into integrated camps, frictions developed. There were fistfights in the beer halls that, in some cases, escalated into fire fights. Regular Army troops had to be called in to separate the combatants. At Entumbane in February, the fighting between Nkomo's and Mugabe's troops got out of hand.

Mugabe made a hard decision. He directed the white commander of the nearby 1st Brigade, Mike Shute, to take whatever steps were necessary to quell what was then described as a "mutiny." Shute promptly committed the Rhodesian African Rifles -- an elite black unit commanded by white officers -- and various supporting units. They put down the mutiny with deadly efficiency. As many as 300 former guerrilla troops were killed at a cost to the RAR of only one casualty, a black sergeant who is now recovering from a head wound.

Mugabe told Parliament: "If they use fists, we will use fists. If they use sticks, we will use sticks. Guns for guns. If it is to be an eye for an eye, we will remove two eyes for one eye . . . . There is still talk of this government as not being representative. There is still talk of revolt. Let us be quite clear that this, my government, cannot put up with these acts of revolt. The sooner they are brought to an end the better."

He also made it clear that he would rely on the old colonial troops to serve as his Praetorian Guard: "We do not have Rhodesian forces anymore. This is Zimbabwe now. Whatever forces there are . . . are all lawful forces." And they proved at Entumbane that their loyalty is to Mugabe. This greatly eases the remaining tasks.

The bulk of Nkomo's troops have now come into the national Army. However, a potentially troublesome force of 5,000 or so troops remains encamped near Victoria Falls at the Gwai River mines. They have heavy armaments, including artillery, armored personnel carriers, Soviet-made missiles and other sophisticated gear. They have taken up defensive positions and would be difficult to; dislodge from the rough terrain they occupy.

"They have two options," a Mugabe military analyst said. "They can return to the bush and try to start a new guerrilla war. Or they can come in and be disarmed and integrated into the new battalions. If they do that, it will draw their teeth and they know it."

There are other problems, none insurmountable.One is financial. The new government agreed last year to pay all former guerrillas a regular soldier's salary -- about $150 a month -- pending their return to civilian life or a regular Army Appointment. The number of men claiming eligibility for these paychecks is estimated at nearly 60,000 -- far in excess of the 35,000 troops believed to have been under the command of Mugabe and Nkomo.

Another problem is that a sizable number of the new recruits are not bringing weapons with them. There is a universal assumption that thousands of rifles, grenade launchers, mortars and other equipment are being cached in the countryside. Countless weapons have found their way into other hands and are being used in the robberies and murders that disturb the peace.

As for the national Army itself, the integration process is proving painful. The number of guerrillas coming in -- about 20,000 thus far -- exceeds the capacity of the Army to handle them.There are insufficient training cadres, inadequate logistical and administrative structures. Some officers complain of political interference that prevents them from applying discipline or discharging unsuitable troops. As a result, white officers are leaving in substantial numbers. With the imminent resignation of Brigadier John McVey, commander of the 2nd Brigade, Brigadier Shute will be the only high-ranking white officer left in the Army.

This exodus does not sit well with many of the regular troops nor with former guerrilla oficers intent on professional military careers. Richard Maluwe until a year ago commanded 3,000 of Nkomo's troops operating in northern Zimbabwe. He is now an officer trainee on McVey's staff. He's upset at the Brigadier's decision to leave.

"The departure of white officers is not a solution to any problem," he said. "There is no need for them to leave. It's their country to defend regardless of any illusions they might have. They have had the experience. They can be teachers for us. If they leave, things will go far less smoothly. They are fair and reasonable. I feel comfortable with them. In any case, this will be my career. I like it."

For all these problems, the official attitude's is one of optimism. Mugabe's intelligence officers are of that view. So is Shute. So are Western diplomats here, including the American ambassador, Robert Keeley.

Maluwe, the former guerrilla officer, expressed a common feeling:

"It's only a question of time before we work it out. We must work it out. The officers in this brigade are doing that. Everyone is exhausted from this war."