Several days after a devastating earthquake shook Mexico City, causing thousands of deaths, police received orders to pull over volunteer rescue workers speeding up and down the streets with horns blaring and red flags flying.

The outpouring of everyday Mexicans willing to help deal with their capital's crisis -- and eager to race through traffic lights on the way -- was perhaps the most obvious immediate political fallout from the Sept. 19 earthquake that has gone down as the deadliest in Mexico City history.

Another tremor, measuring 5.0 on the Richter scale, shook Mexico City for less than a minute late Friday night, causing buildings to sway and panic among residents, but there were no reports of new casualties, according to news services.

In a capital notorious for a powerful bureaucracy and a passive population, the people seemed to rise to the occasion more vigorously and swiftly than the city or national government. In the first few days of rescue efforts, for example, students and other volunteers spontaneously climbed into the rubble in search of victims while others used their cars as ambulances to ferry the injured to hospitals.

They often worked at considerable risk without orders or official supervision. Sometimes the volunteers worked while Mexican Army troops stood idle with G3 rifles in their hands, guarding against looters who never seemed to come.

As the first shock of disaster wears off, Mexicans have begun to grumble, perhaps inevitably, about how President Miguel de la Madrid's government responded to the gravest national emergency it has faced since his election three years ago.

Attention has focused quickly on the political consequences of Mexico's tragic earthquake because a similar disaster in Nicaragua in 1972 became as a factor in President Anastasio Somoza's downfall to the Sandinista rebel movement 6 1/2 years later.

The Nicaragua of Somoza in 1972 was vastly different, however, from the Mexico of de la Madrid in 1985. In a demonstration of the unusual political system that has evolved over decades in Mexico, the griping here seems so far to center on the bureaucracy rather than the political leadership embodied by de la Madrid and his Institutional Revolutionary Party.

This reflects the peculiarly Mexican political atmosphere in which the party has truly become institutional, anchored by a half century of uninterrupted rule. Its leader, picked by his predecessor and then ratified as president by elections, assumes an almost noble remove that reduces or at least lessens the impact of political or popular nagging.

In addition, de la Madrid has seemed to exhibit a concern and presence enhancing his role as the country's leader, appearing on television shortly after a second earthquake and making daily tours of the hardest-hit neighborhoods. A number of Mexicans commented that the president, ordinarily a stiff figure with a remote style, seemed more familiar and at ease than ever before as he sought to reassure the people.

Observers with long experience here warned that the president still faces the challenge of demonstrating that he can move the bureaucracy into helping people deal with the consequences of disaster over many months. Otherwise, they added, an already perceptible estrangement from entrenched and often corrupt government offices could develop into political bitterness with dangerous long-term repercussions for de la Madrid or his successor as head of this nation of nearly 80 million.

The task cannot be easy. While Mexican officials have not calculated total earthquake damages, the National University's Engineering Institute has put them at $2 billion.

Mexico already pays an estimated $12 billion a year in interest payments on its $96 billion debt. The $1 million gift check brought this week by Nancy Reagan would have been spent on interest alone before she left the city if it had been intended for Mexico's long-term financial problems.

Although by American standards de la Madrid's personal appearances were modest and his visibility low during the week of crisis, Mexican political traditions and de la Madrid's success in striking the right tone on television so far have left the bureaucracy that few love anyway as the main target of public criticism.

"Now that it has quaked, a number of bureaucrats have shown their abilities to the people," said one man in a cartoon in the liberal newspaper Jornada. "And now that a number of bureaucrats have shown their abilities, the people have quaked," responded a second figure.

Some of the quaking is being done by former residents of the Nuevo Leon government apartment building, which collapsed with the loss of hundreds of lives. Survivors have been lining up daily at the National Popular Housing Fund, many of them wearing casts and bandages, to demand more help getting along until they find new houses or apartments. They also complain that warnings about flaws in the construction were ignored before the earthquake.

"This is the responsibility of the federal government and the whole country, not just us," the fund's director, Enrique Ortiz, told reporters who asked about the demands.

His bucking of responsibility toward the national government, ultimately to the president, illustrated another source of contention underlined by Mexicans and foreigner observers. Unlike most other large cities, this sprawling capital is governed by appointed officials, without any elected city council or other representative body. The lack of accountability has intensified the tendency to put the bureaucracy at the center of public resentment, they said.

Luis Carbajal of the Mexican Workers Confederation, the ruling party's national labor organization, reported another source of public wrath well known in Mexico. He told the newspaper Jornada that police from the Mexico City federal district seeking bribes are holding up truckloads of relief supplies from outlying provinces. In addition, diplomats reported some foreign aid arriving at Mexico City's giant airport was stolen before reaching earthquake victims.

Mexicans have speculated widely as well about possible corruption in implementation of building codes, contending that some buildings collapsed because of shoddy materials while neighboring structures held firm. The Unified Mexican Socialist Party, the country's communist organization, has declared that it will seek a legislative investigation and Mexico City's appointed mayor, Ramon Aguirre, announced a separate administrative inquiry.

Other grumbling has centered on what many Mexicans and foreign specialists saw as lack of coordination in rescue efforts. Mexican officials at one of the most tragic sites, clothing factories where hundreds of seamstresses were buried under rubble, were still arguing about who was in charge a week after the earthquake. Other examples around the city prompted the newspaper Excelsior to write, without tracing responsibility beyond a faltering bureaucracy:

"Lack of water threatens to set off epidemics and distribution of the liquid is deficient; aid is not distributed rightly among victims; there is too much heavy machinery in some places and not enough in others; lists of those buried, injured, disappeared and supposed trapped alive are duplicated, triplicated and quadrupled, causing confusion."