A rash of wildcat strikes and student violence in Rhodesia has confronted the country's socialist leader Robert Mugabe, landslide victor in last month's elections, with an unexpected and embarrassing challenge even before he assumes power.

Mugabe's officials have been puzzled and concerned by the unrest, the most severe of its type here since 1952, because it comes too soon after Mugabe's Zimbabwe African National Union party won overwhelming support in last month's British-supervised elections and even before it has had an opportunity to show what it intends to do for black workers in a country emerging from 90 years of white-minority rule.

The officials are in an awkward position to deal with the strike because although they already have been named to their Cabinet posts, they do not officially come to power until the British governor, Lord Soames, declares this last British African colony independent on April 18.

In an attempt to deal with the workers' discontent, Mugabe's officials, including the minister-designate of labor, Kumbirai Kangai, have visited the affected firms to discuss the strikers' grievances with them. In most cases, they have convinced them to return to work.

It is still far from clear why the worker unrest, which caught even black trade union leaders by surprise, broke out at this time. But Kangai has dismissed the possibility that a conspiracy was the cause of the mostly unorganized unrest.

However, a South African newspaper quoted a source close to Mugabe yesterday as saying, "These people are obviously being used as puppets. The government should take rough measures against these people. They are doing this for no other reason but to embarrass the new government."

The labor unrest first cropped up in five firms last Tuesday. By Friday, 23 other business concerns in the industrial, mining and farming sectors had experienced strikes, involving at least 5,000 and possibly as many as 8,000 workers, according to figures supplied by the Information Ministry. Demands included higher wages, shorter working hours and in some cases, return of pension fund contributions.

In the town of Gatooma, about 350 black municipal employes brought services to a halt when they walked off the job, forcing the National Guard to take over their tasks, according to the Information Ministry.

By late Friday 2,400 workers had been fired and 384 were still out on strike. The remaining had returned to work after negotiations with their employers or with Mugabe's party officials. None of the strikes involved violence.

Meanwhile, black students at four black private schools in Salisbury stoned their school buildings and in one instance set fire to school furniture after demanding a reduction in fees, according to the director of the private schools, Robert Marple. Black teachers at the schools went out on strike demanding a 90 percent increase in wages.

"We've never experienced this type of [violent] approach before," Marple said.

One black manager said he found it unusual that the workers were demanding the return of their pension fund contributions when they had so many other more immediate grievances related to wages and working conditions. The demand was made by workers who said they feared the government was going to nationalize their pension funds, an idea that Kangai labeled a "malicious lie."

Mugabe's election victory came despite a campaign by the white-minority government and his black rival, former prime minister Fbishop Abel Muzorewa, to paint him as a hard-line Marxist. He has gone out of his way, however, to emphasize that pensions will be guaranteed.

A white industrial leader called the unrest "most peculiar."

"It's difficult to describe; it's almost eerie because it's been so calm. It's almost as though it's not real that it's a charade. The workers behaving in a funny fashion. In many cases we ask 'who is your spokesman?' and they say, 'Nobody, we're all speaking' -- and then they go home," the industrialist said.

The strikes concerned him because they come as Western countries are discussing giving aid to Rhodesia and business leaders in the formerly sanctions-bound country are hoping to attract large amounts of Western investment capital.

"What better way to stop it?" the white businessman asked.