Nobody has seen anything like this since the end of the Vietnam war: sit-ins, teach-ins, class boycotts, mass arrests.

Here at Berkeley, where the Free Speech Movement brought nationwide attention to student protesters in 1964, more than 100 students have spent every night this week in sleeping bags on the steps of the University of California's administration building.

At Columbia University in New York, protesters evoked memories of 1968 by chaining shut the front doors of Hamilton Hall. They refuse to leave the front steps until the university sells about $34 million of its financial interests in firms that do business in South Africa.

"For the first time I'm proud to be a student," said Susannah Kennedy, a political science major at Berkeley. "I'm proud to be an American student. It's like -- maybe we're not all becoming yuppies."

But they show little sign of becoming hippies, either. "We were children in 1968," said Vilna Simmons, a member of the student committee that planned the protest at Columbia. "We're not doing this as a repeat or rerun of 1968."

The issue is South African apartheid, and what it is stirring up on campuses this month has startled professors grown accustomed to the celebrated student conservatism of the 1980s. Columbia students are calling their administration building the Nelson Mandela Center, in honor of the imprisoned black South African leader of the African National Congress. In New Brunswick, N.J., from 80 to 100 students have spent the last week occupying the Rutgers University student center, which they are calling the Nelson Mandela Center. In Santa Cruz, 100 students at the University of California's campus there are sleeping on the floor of their administration building and calling it Winnie Mandela Plaza, in honor of Mandela's wife. And in Ithaca, N.Y., more than 100 Cornell University students marched on Thursday into the administration building and renamed it Steven Biko Hall, in honor of the black South African activist who died in police custody eight years ago.

There was a rally at Georgetown, a rally at Brown, a rally and vigil at the University of Pennsylvania. At the University of Michigan, students have planned demonstrations for this weekend, and students at a number of campuses have passed fliers calling for a national boycott of classes next Wednesday. At the University of California at Santa Barbara, famous for its devotion to sunshine and beer, a campus spokeswoman murmured, as she searched her desk for notes on last Wednesday's student demonstration there, "Here we have it, finally. An issue for the '80s."

Students at nearly all the campuses have presented their administrations with demands similar to those of the Berkeley protesters -- that the universities rid themselves of investments in companies with subsidiaries or business dealings in South Africa. Divestment is a controversial proposition among institutional investors, who argue both its economic and political merits.

It is the moral clarity of the cause that attracted many of the students who cut classes to crowd into Berkeley's campus plaza this week. It is like no political issue they have ever encountered, and they seem exhilarated by their own response.

Five thousand students, many of them scrambling onto tree branches or rooftops for a better view, crowded into Sproul Plaza Wednesday afternoon to chant, to cheer speakers, to listen and to join in on spontaneous heated arguments between strangers. And at dawn on Tuesday, campus police arrested 159 of the people sleeping in front of the administration building. When asked for their names, 29 of those arrested identified themselves only as "Steven Biko."

Peter Linde, a 21-year-old history major taking part in the all-night vigil, said: "Sure, there's a desire to escape the narrowness of your life, and here's an issue that in a very short time a lot of people have been sensitized to and learned a lot about. And I think they feel good."

He added that when he first came to Berkeley, a decade after the antiwar movement was at its height, "I sort of felt like, 'Oh, boy, I really missed out.' That was the time to be here, when there were sit-ins and all that."

"You just get so sick of being told how apathetic you are, and how career oriented you are," said John Searle, a Berkeley campus philosophy professor who believes divestment would have no effect except, as he put it, "to force the university to shoot itself in the foot."

"It's sort of like the reawakening of the Vietnam thing, when you had war on the TV news every night," said Steven Segal, a Berkeley professor of social welfare. "In the past several weeks, you've been unable to not be aware of it. The pictures have been vivid."

But unlike the blurred issues of the Vietnam era, divestment is a particularly tidy and accessible issue, neither as troubling as domestic economic policy questions nor as distant as most debates over American foreign policy.

And unlike the 1960s, there has been little outraged rancor or violence.

Seventeen years ago at Columbia, for example, students occupied Hamilton Hall in the center of campus, kidnaped a dean and engaged in violent combat with helmeted, club-swinging police sent to restore order.

Now it is a genteel kind of protest; anyone wanting to enter Hamilton Hall can use a back tunnel. Some students catch up on their reading during their picketing. And talk of "nonviolent" civil disobedience has replaced the defiant threats of confrontation.

Inevitably, the comparisons abound -- underscored by the folk songs of Pete Seeger and chants of "We Shall Not Be Moved." Even some of the faces are the same; Columbia President Michael Sovern was one of the administrators negotiating with the students during the 1968 uprising. Some faculty members who joined the 1968 barricade once again are organizing their colleagues in support of the students.

But to those at the school both then and now, Columbia 1985 is a far cry from Columbia 1968. The support now is smaller, the times less heady, the issue more intellectualized and the movement more diverse and less torn by internal turmoil.

"This situation is not as chaotic and crisis-ridden as in 1968," said history Prof. Eric Foner, who has sympathized with the students in both protests. "Nineteen sixty-eight was the culmination of years of student frustrations over a wide range of diverse issues -- the civil rights movement, Vietnam, the archaic structure of the university."

One difference is the clear definition of the issue.

"I don't usually grab a sign or sit in a protest for something that's really intangible," said Scott Flicker, a 21-year-old philosophy senior at Berkeley who wore a small red ribbon, a symbol of support for divestment, pinned to his sport shirt. "It's so clear-cut. Doesn't it seem clear-cut? Of any place in the country, a university should have a moral stand. If you asked me whether the U.S. or the entire world should pull their investments out of South Africa, I'd have to think a little further, because that might topple the government, which might lead to violence, and I'm not sure I'm ready for that."

In New York, Barnard College's Peter Juviler, a political science professor, said that unlike the 1968 protests, which produced a split between black and white students, these have been marked by "much more inclusiveness, in terms of background and ethnicity."

This protest also comes at a time when college students nationwide have come to be viewed as increasingly conservative and concerned more with schoolwork than with sit-ins. This trend was evidenced by the almost overwhelming support President Reagan received on college campuses last November.

This antiapartheid protest, however, does not seem to presage any new student activism. "These students are all preprofessional," said Dennis Dalton, a Barnard political science professor who has seen past Columbia sit-ins. "You see among these students a real stress you didn't see in 1968 or 1969. They want to go to the best medical schools and business schools, and they know the way to do that is to not get arrested and stay in the mainstream."

Perhaps as a consequence, this protest on its face has been free of the beer, pot and "Off the Pigs" sloganeering that marked the 1960s demonstrations.

"We've been telling people, 'No drugs, no alcohol,' " said Columbia sophomore John Klavens. "This is not like some counterculture sit-in on the steps."

At Berkeley, the chilly two-hour outdoor meetings every night may have been punctuated with obscenities, but also with loud calls for parliamentary procedure.

The protesters have asked university officials to move from June to May a meeting at which the regents who govern the university have promised to examine the divestment issue. This is not the first time the issue has been raised before the regents; an earlier request for divestment was rejected eight years ago.

A lot of money is at stake. By its own estimates, the nine-campus University of California keeps $1.7 billion of its $5 billion investment portfolio in companies with ties or business in South Africa. Four billion of that total figure is retirement funds for university employes, and it has been argued that any change in the investment policy, no matter how politically well intentioned, might result in a loss of money for retired university personnel.

And, said one Berkeley student: "If the chancellor walked out today and said, 'Okay, I just divested' -- would all these people be happy? I don't know. There's a lot of people out here who like the idea of the protest . . . There's a legacy here at Berkeley, with the Free Speech Movement and all that stuff . . . I think students are ready to use just about anything as a pretext."

The students and the faculty members supporting them seem convinced that unlike some of the causes of the '60s, divestment is a fight that can be won through an organized, highly visible protest.

"This is not 1968," said Barnard's Dalton. "The apartheid issue is different from Vietnam. This is something we can do something about. We have it within the power of our community to change things this time."

For American students, the issue was a long way away.

But at Columbia, Jose DeSousa, a black South African student, brought it all home to them when he learned the price he might have to pay for participating in the protests.

On Wednesday, DeSousa, 23, got a telegram from Pretoria, saying his mother and brother had been detained by South African authorities for three days. DeSousa says they were questioned about his antiapartheid activities and were shown a warrant for his arrest.

"I expected they would mess around with me but not with my family," said DeSousa, a biochemistry major who expects to graduate in 1987. "I feel bitter and powerless and shocked."

Sitting on a worn-out mattress in the room where he had fasted for 15 days, DeSousa said he had been charged for participating in communist activities. If he ever returns to South Africa, he said, he would be arrested and charged with high treason. The penalty would carry a minimum of 20 years in prison and, at worst, a death sentence.