One recent sunny day Phyllis Tahome, 36, bundled her children into a bus and then aboard a train for a trip to one of South Africa's beautiful beaches in the Cape Peninsula.

They were not at the beach long, however, when they became victims of the South African racial segregation scheme that "allocates" the sky, sea, sand and surf of its magnificent coastline to separate races.

A policeman told the Tshomelas they had to leave the beach because they are black and the beach is for whites only, even though the nearest black beach could be reached only by car.

It is "beach apartheid" that makes the coast of Durban look like a "Dagwood sandwich" when seen from the air.

The blacks are all congregated at one end of the shoreline where a sign says, "African beacn." Adjacent to them are the seperate beaches for "Coloreds" (people of mixed race), and then the beach for Indians. Finally comes the "whites beach" for those endeavoring to become as brown as those on the three other beaches.

Blacks and Coloreds who holiday in Durban find they can frequent the "international hotels" and "international restaurants" that serve all races, but when they want to swim, they must to to the segregated "African beach" or "Colored beach."

Most of South Africa's coast along the Indian and southern Atlantic oceans is "undeclared," that is, not allocated to any one race. "You know, like what a beach is supposed to be," said a resident. But these undeclared beaches are far from population centers and without public transport, and swimming in many cases is not possible because of rocks.

"Beach aparthied" is the result of the ruling National Party's philiosophy of keeping racial groups separate to "avoid racial friction." Opponents of beach segregation say it is the separation of the races that causes the friction.

Nothing illustrates better the National Party government's failure to fulfill its promise of eliminating unnecessary racial discrimination than this issue. Although much of the white population would support the scrapping of beach apartheid and although it is a sphere that does not vitally affect people's lives, the national government has not yet proded the conservative forces in coastal areas who support the segregation scheme.

Ever since beach apartheid was introduced in the 1960s opposition politicians have regularly called for its abandonment, but their pleas have been ignored. In Cape Town, for example, the city council, dominated by opposition Progressive Party members, refused to "allocate" its beaches, so the provincial government, dominated by National Party members, put up the signs and sent the bill to the city.

Lately, however, because of genuine overcrowding and growth of the black consciousness movement, beach apartheid is breaking down. Coloreds and blacks appear on white beaches - sometimes they are asked to leave, and sometimes the aren't.

Cape Town beach constable Willie Geldenhuys has another explanation.

"It's the Jewish people, they're coming up for the Coloreds," he said, referring to the predominatly Jewish population of some Cape Town suburbs who traditionally support the antiaparthied Progressive Party.

Every Sunday Geldenhuys can be seen on the beaches sweating in white shirt and tie, with his two-way radio slung over his shoulder. Geldenhuys passes out summonses for dogs without leashes, and for ball playing, but on city council orders he forgets about beach apartheid. If everybody is getting along in mixed company, he is to let them alone.

This relaxation does not please everyone.

"There's no white beaches any more," said a white woman who refused to give her name. "They want to do away with it because they're being egged on by Communists."

There are objections even in the Miami-type beachfront communities which are represented by the opposition politicians who are calling for an end to beach apartheid.

These compliants are against the "hooligans and unruly elements," who have begun to invade the beaches.

They say they want to deal with the 'riff-raff' problem, but because of the short-circuiting that goes on in the brain, it comes out as a black and white problem," said a newspaper reporter.

Many whites, however, echo the sentiments of a white school teacher who said. "I wouldn't mind if beach apartheid were scrapped."

Among the Colored and black population there is both continued resentment and quiet acceptance of beach apartheid. Francis van Rensburg, a black personnel supervisor, drove down from Johannesburg with his family for a holiday in Cape Town.

When they saw only white people at the first beach they stopped at, they decided not to venture out on it, "in order not to cause unnecessary racial friction," Van Rensburg said sardonically.

A 30-year-old Colored woman who works as a maid, when asked how Coloreds feel about beach apartheid, said: "They smile but inside they don't like it. You wonder how long they can go on holding it in."

Frederick Truter, 31, a Colored hardware salesman, who was asked to leave a white beach, said, "I don't understand beach apartheid it's the same tide."

The dangers of the sea are also the same. When a skull was found recently inside the stomach of a shark, it was not clear whether it was the skull of a white man or a black man. (Sharks swim at all beaches).

The local magistrate sent it to the anatomy department of a nearby university medical school to determine the race of its unfortunate owner so the authorities could decided where to bury it - in a black or a white cemetery.