SEOUL, JUNE 27 -- In the Philippines, the demonstrators had Corazon Aquino. In Iran, they had the Ayatollah Ruhollah Khomeini. In South Korea today, protesters are flocking to the streets against a deeply unpopular leader too, but they have no real idea of who should come next.

It is not that South Koreans reject the notion of leaders. Their political culture, in both government and op-position camps, is based on concepts of rigid centralized authority. In everyday parlance here, leaders do not take office, they take power.

Rather, the fact is that the long-fragmented and feuding opposition has yet to offer a political figure capable of generating mass enthusiasm with the new generation of Koreans.

Old-guard opposition politicians Kim Young Sam and Kim Dae Jung are attempting to ride the wave of public sentiment unleashed against the government in three weeks of street protests.

But neither man seems to command widespread enthusiasm or to control the direction the movement will take. They retain strong control of the main opposition party, blocking the rise of younger men.

Ordinary Koreans are placing their faith instead in the ideals of democracy, a system under which they have never lived but that seems to them a political cure-all.

"If change comes, who the leader is will not matter," said a Seoul shopkeeper. That problem will solve itself through the democratic process, he added.

For the time being, the political pot bubbles along, heated by popular hostility toward President Chun Doo Hwan.

In a negative sense, it is Chun who is the opposition leader, the man who provides focus and keeps together an inherently unstable coalition that includes students, activist clergymen, politicians and a grab bag of other groups.

South Koreans find it easy to dislike the stern-faced man who lives behind mammoth security in the Blue House, as the presidential compound in northern Seoul is known.

He has a reputation for talking rather than listening, running affairs of state in the style he acquired during a military career. He is humorless. Korean class prejudices also work against his standing in the cities: soldiering has never been a respected occupation here, nor has the farming his parents practiced.

Almost every night, government television news shows broadcast lengthy scenes of Chun touring schools and government offices, surrounded by obsequious aides, lecturing Koreans on the virtues of hard work, vigilance, honesty and other traditional values.

Chun is deeply resented for demanding that people treat him like a philosopher-king in the Confucian mold when in their eyes he has done nothing to earn it.

Legitimacy is a constant theme in the traditions of government here. Many South Koreans said Chun shot his way into office as an Army general during the 1980 uprising in Kwangju city, where more than 200 people were killed, and has remained there primarily through force.

On June 10, Chun's ruling party nominated his military academy classmate Roh Tae Woo to run for president in an election Chun had planned for late this year. That touched off the current wave of demonstrations, putting Chun's whole succession timetable in jeopardy.

Roh is condemned as being just a stand-in for Chun. He is sometimes called "the bald man with a wig."

But neither do the two Kims of the opposition have a pristine image. Professional politicians are regarded as untrustworthy by many Koreans.

For more than two decades, the Kims have been fighting nonstop to get power. While many Koreans admire their fighting spirit, many assume that ambition drives them as much as concern for democracy.

They are recognized as courageous men who have perhaps had all the good will squeezed out of them by oppression they have faced over the years. They run their party as tightly as Chun runs his, making some Koreans wonder whether having one of them in the Blue House would really change anything.

"Since we don't have better leaders for now, we let them speak for us," said a student at Seoul's Yonsei University. "They are politicians. They are very much eager to grab power."

Most South Koreans do want change in their government. Increasingly well educated and affluent, they are aware and a bit ashamed that their country is seen abroad as stunted politically, despite its many impressive achievements in the economic field.

They want a government that is more open and legitimate, that does not try to suppress dissent. Above all, they want the knowledge that freedoms they have do not exist at the sufferance of one individual.

Each step forward in the economy means people have more to risk, however. The middle class, and most people consider themselves a part of it, is in general genuinely fearful of what the government likes to call "social confusion," the breakdown of law and order.

Yet hatred of the Chun government is so strong these days that people are willing to risk a bit. While they may not join the demonstrators, there is near universal sympathy for them and their objectives.

"I have no courage to go out and throw rocks," said the Seoul shopkeeper. "But that may be what is needed to get the government's attention."

Students here, like those everywhere in the world, are more willing to take risks and have more rigid views of politics. A few are leftist ideologues who espouse creation of a workers' state in South Korea and want to "drive out" the United States. Most, however, prefer the center, espousing a vague form of democracy and, in many cases, redistribution of wealth.

"The students' goal is first to put an end to military dictatorship and second to establish democracy," said the Yonsei University student. Many students say the same thing, but few seem to have firm ideas of how the new government would be structured and by whom.

The two Kims are the names that come up most often as opposition replacements for Chun. But they would run up against another reality of the political world here, the veto power exercised by senior officers in the armed forces.

The 600,000-member military is a highly disciplined fighting force that plays no direct role in day-to-day politics. But by common understanding, anyone who sits in the Blue House must have its seal of approval.

Kim Dae Jung is considered a communist revolutionary by a good many officers. Kim Young Sam has a somewhat less negative image. Still, his frequent statements that the threat from communist North Korea is overblown cannot have won him many friends in the ranks armed forces.

One man sometimes mentioned as a long-shot compromise is Kim Jong Pil, a prime minister under former president Park Chung Hee. This third Kim is now living in semiretirement here, but retains loose affiliations with the minority opposition Korea National Party. The logic is that he would be acceptable to both the military and the middle class. With his ascendancy, objections from students could be ignored.

However, no one here sees the Chun government as on the brink of collapse under the demonstrators' pressure. But as of Feb. 25, 1988 -- the day his term ends and the day he has promised to step down -- draws closer, South Koreans will spend more and more time wondering who their next president will be.