Over the centuries, life in this ancient city traditionally has revolved around its imposing hilltop citadel and the maze of narrow alleys, old stone houses and covered markets surrounding it on all sides.

It was here that residents of Aleppo, who claim theirs is the oldest continuously inhabited city in the world, rallied to resist a succession of invaders including the ancient Persians, Byzantines, Arabs, Crusaders, Mongols and Ottoman Turks.

Today, the old quarters that stretch out below the high stone walls of the moated fortress are the stronghold of a new resistance.

These quarters are the preserve of the Moslem Brotherhood, an outlawed clandestine organizatrion of Islamic religious extremists that has been waging a relentless campaign of political assassination and terror against the Syrian government of President Hafez Assad.

Because of this campaign, parts of Aleppo's old souk, or market, and some downtown streets are places where high government officials and security agents fear to tread.

The activities of the Moslem Brotherhood and other organizations here like it have helped put this northern Syrian city in the forefront of opposition to the government in Damascus.

While residents say that rumors in the capital have exaggerated the troubles here, they confirm that there has been more violence in Aleppo than elsewhere in the country.

[In the latest incident, Syrian security forces killed eight members of the Moslem Brotherhood Monday in a gunbattle in Aleppo, the official Syrian news agency reported from Damascus. The agency said quantities of automatic rifles, grenade launchers, handguns and other weapons were found in a house that security forces raided at dawn.]

For several weeks late last year, residents said, shooting incidents occurred with increasing frequency and the sound of gunfire resounded almost every night through nearly deserted streets.

The number of security forces killed in hit-and-run attacks aroused serious concern in Damascus, according to diplomats.

The attacks slowly chip away at the government's authority and might embolden other opponents to rally behind resurgent Islamic fundamentalism, as represented by the Moslem Brotherhood.

In addition, if the attacks continue, Syria's Alawite rulers fear the country could be drawn into a bout of sectarian strife akin to that in neighboring Lebanon. Such a development would add a destabilizing element to Middle East peace moves and would undoubtedly alarm Syria's neighbor to the southwest, Israel.

In response to the violence here, the government at the beginning of the year sent as many as 3,000 special forces and regular Army troops to Aleppo in a show of strength. The troops conducted house-to-house searches in some neighborhoods in an effort to root out antigovernment guerrillas.

How successful they were remains unclear, but residents said the shooting had tapered off lately and the troops were recently pulled out of the city proper.

Another government measure against the opposition has been to substantially increase the local strength of the Syrian secret police and intelligence organization.

Most of the secret police are said to be members of Assad's Alawite Moslem sect, whose domination of the country has incurred the wrath of many adherents of the majority Sunni Moslem sect.

This resentment has fueled support for the Moslem Brotherhood, which represents a fundamentalist strain of Sunni Islam. Active in Egypt in the 1950s as a counterforce to president Gamal Abdel Nasser's "Arab socialism," the Brotherhood today has independent chapters in a number of Arab countries. These groups usually are further to the right than even the most conservative Arab governments and are widely outlawed.

In combating the Syrian government the Brotherhood not only is trying to supplant a minority Moslem sect but is battling policies of the ruling Arab Baath Socialist Party, under which Assad has fashioned a secular socialistic government oriented toward the Soviet Union.

Why Aleppo should have become a hotbed of violent opposition to the government elicits a variety of explanations here.

One is that it is simply easier for guerrillas to operate here because there are normally far fewer security forces than in the capital. The security forces, for example, have never been up to the task of controlling prosperous smuggling operations here and a variety of weaponry is available in parts of the souk to which strangers are not admitted.

Another factor in the guerrillas' favor is that Aleppo, a center of commerce and industry in its own right, traditionally has had a rivalry with Dasmascus. Proud of their heritage dating from the third millenium B.C., many Aleppines believe that their city, and not Damascus, should have been the Syrian capital. Both cities have populations of about 1 million.

Although Aleppo is relatively prosperous by Syrian standards, according to residents here, the Moslem Brotherhood has been able to capitalize on discontent arising from the Baath Party's economic policies, which emphasize the public sector and tend to run against the grain of the Aleppines' entrepreneurial spirit.

The Moslem Brotherhood is said to have made considerable inroads with merchants in the souk, who resent government restrictions on profits, cash transfers and imports. Even so, some residents were surprised to learn recently that two sons of one of Aleppo's wealthiest families were members of the Moslem Brotherhood. One was killed by security forces and the other has gone underground.

Except in such cases when people are killed, arrested or forced into hiding, little is heard about the Brotherhood's membership, and its numerical strength remains a mystery.

Some analysis believe the group may count only a few hundred hardcore guerrillas throughout the country operating in small cells that are hard for government agents to penetrate.

The often random nature of the attacks attributed to the group have aroused considerable criticism from liberal and leftist Syrians who also oppose the government.

The biggest single operation attributed to the Moslem Brotherhood was the massacre last June of 70 cadets, most of them Alawites, at a military academy near here. In addition, at least five local religious leaders have been assassinated for speaking out against the organization.

The fear, raised by the prospect of getting on the Brotherhood's enemies list has spurred some Aleppines to new heights of enterprise. In one of several such instances, a wealthy Armenian businessman here last week received a letter purporting to be from the Moslem Brotherhood and demanding payment of $5,000.

"Everybody's trying to get into the act," a diplomat here said.

In another case, an Aleppine with marital problems received a death threat signed by the Brotherhood and hastily left town. Some wags here suggested that his wife had probably written it.