If the Cape Town bombings are meant to convey a political point, the message is unclear. If the pipe bombs are intended for a particular target, none readily comes to mind.

A bombing in August 1998 killed two people at a Planet Hollywood waterfront restaurant known largely as a tourist attraction. Early this month, a pipe bomb exploded in a pub that is known as a hangout for gay men. And the most recent bombing occurred Sunday inside a pizzeria that is frequented mostly by families with young children.

Eighty pipe bombs have exploded over the past year in Cape Town, and no one has claimed responsibility for any of them. The suspense of who is behind the bombings, and why, has become both a national mystery and an affront to a country that is proud of its mostly peaceful transformation from white minority rule to an authentic democracy despite its international reputation as a violent and dangerous place.

"Cape Town is in a sense the keyhole through which the outside world views South Africa," Nick Boraine, an analyst for the banking firm HSBC, told the Reuters news service today. "If this doesn't happen again, we can weather it. If it does happen again, we are in deep trouble."

South Africa is battling its image as it tries to attract much-needed foreign investment. And public officials are relying on the reputation of Cape Town--the city that South Africans prize more than any other for its spectacular setting among two oceans and a mountain--as one of Africa's most popular tourist spots to bolster its struggling economy.

Sunday's bombing inside the crowded St. Elmo's pizzeria injured at least 43 customers and workers, including several who lost limbs. Police say they believe the homemade device was placed in a plastic bag underneath a table inside, and they say that a cell phone was used to detonate the bomb, the first time that such a method has been used to trigger one of the explosions.

Police suspect that a radical religious organization, which is known for organizing vigilante groups to punish and even kill criminal suspects, is responsible for the bombings. But no arrests have been made, the group has denied the charges and any motives for the violence remain speculative. Police have formed a special investigative unit and officials have offered a reward in excess of $200,000 for information leading to an arrest.

South Africa has been largely free of political violence since just before the first all-races elections in 1994, when right-wing extremists planted bombs in an attempt to undermine the democratic process. Those attacks failed, and, many here say now, only served to galvanize the public even more.

"That's why these seem so strange, and almost anachronistic," said Bernard Mogase, a sales representative in Johannesburg. "We thought we had put all this foolishness behind us when we went to the polls five years ago. What can anyone hope to prove now by putting a bomb inside a crowded restaurant?"

The bombings prompted South Africa's top law enforcement official today to propose anti-terrorist legislation modeled after U.S. laws passed after the bombing of a federal office building in Oklahoma City in 1995 killed 168 people.

Civic officials are concerned that the bombings will dampen tourists' interest in Cape Town. The city is usually crowded during the holiday season and officials expect that millennium celebrations--including a party hosted by South Africa's revered former president Nelson Mandela--will attract more tourists than usual.

CAPTION: Traumatized workers hold their heads after the most recent pipe bomb explosion, at a Cape Town pizzeria on Sunday, injured at least 43 customers and workers.