An explosion in a central square of Kabul that signaled the start of the Soviet military takeover of Afghanistan just two years ago Sunday is still reverberating around the world.

The invasion has tarnished the image of the Red Army, which in its first real long-term military test since the end of World War II remains tied down by ragtag bands of nationalist rebels. In a succession of votes in the United Nations, the nonaligned movement and the Islamic Conference, the invasion has punctured the Soviets' carefully cultivated image as a friend of the Third World; some analysts think that by tying down Soviet troops, Afghanistan serves as a restraint against Soviet military action in Poland.

In two years, the Soviets have failed to gain either political or military control of Afghanistan despite the presence of as many as 110,000 troops in that rugged, Texas-sized nation.

Until recently, most Western diplomatic sources had placed the Soviet troop strength in Afghanistan at 85,000. Now there is a growing feeling among both Asian and Western intelligence experts here that the Soviets are increasing this number. One source placed it at 110,000--the number cited about six months ago by a Western diplomat but immediately denied by the Pentagon in what some here saw as a move by the Reagan administration to dampen anti-Soviet feeling before keeping a campaign promise to end the grain embargo.

Washington, which keeps close watch on Soviet troop movements in Afghanistan through satellite surveillance, now says there are at least 90,000.

The State Department said Saturday that "the Soviet occupation forces and their Afghan puppets are today no closer to their objectives of suppressing the resistance and establishing firm control of Afghanistan than they were two years ago."

The statement, describing the Soviet forces as bogged down in their battle against the Afghan nationalists, warned that "there is growing concern" that pressure to produce military results "will lead to an increased use of chemical warfare by the Soviets." It said "evidence of the use of lethal and casualty-producing chemical agents is mounting," and the main use has been against rebel bases in caves, "which are otherwise inaccessible to aircraft or helicopter attack."

Meanwhile, the Afghan Army, which Moscow hoped would carry the bulk of the fighting with Soviet air support and advisers, continues to shrink. It is now estimated at 30,000 men--one-third its strength at the time of the Soviet invasion--while the rebels are widely believed to be better armed now than they were two years ago.

The Afghan government's draft calls are ineffective and many of those conscripted appear to drift away with their weapons to join rebels before they even taste combat.

Soviet Deputy Defense Minister Sergei Sokolov is reported to have been in Kabul this winter to reassess the military situation, in which nationalist rebel bands--although so disunited that they often fight battles among themselves--control about 80 percent of the countryside.

Western and Asian military analysts report that even the Soviet Army has not done well in its battles against the rebels.

Soviet military strategy is reported as static and unable to meet the challenges of a guerrilla war. Many of the Soviet weapons--with the MI24 helicopter gunship and advanced-design, lightweight armored personnel carriers as notable exceptions--are hampered by the mountainous terrain, with its lack of good roads and easy cover for guerrilla fighters who know the country.

Discipline is said to be slackening in the Red Army. Diplomats report that Soviets are trading equipment for drugs, and soldiers have been seen selling used military shoes and scarce gasoline from Army trucks in downtown Kabul.

Estimates on Soviet casualties vary, with the Pentagon placing the two-year toll at about 5,000 killed and 5,000 wounded.

While the state-controlled Soviet public-opinion apparatus has kept this toll from becoming a major domestic issue, the political cost in the rest of the world appears high. It remains a serious irritant in U.S.-Soviet relations and gives Moscow a negative image among nonaligned and Islamic nations.

Each year at the United Nations, anti-Soviet resolutions on Afghanistan pass by greater margins, even though Moscow mounts a peace offensive each time in an apparent attempt to blunt the damage.

The tentacles of the resistance fighters extend even into the Soviet stronghold of the capital city of Kabul, where Soviet soldiers reportedly have been forced to resume 24-hour guard duty in an attempt to stem rebel attacks.

Explosions go off day and night in Kabul's public places including, according to Western and Asian diplomatic reports reaching here, one in the former Kabul Intercontinental Hotel during an Afro-Asian solidarity meeting late last month.

The rebels reportedly move so freely in Kabul that a Soviet civilian technical expert was kidnaped from the streets and now is being held for ransom by nationalist forces in the rugged mountains near the eastern border with Pakistan.

The rebels operate their own radio station, Radio Free Kabul, which was heard in the Afghan capital for the first time two week ago. It broadcast 30 minutes of anti-Soviet propaganda and threats against pro-Moscow Afghans over a transmitter reportedly donated by Western European supporters of the Afghan resistance.

Although there is no question that some weapons--especially the antitank rocket-propelled grenades that have become the latest prestige plaything of nationalist guerrillas--are being supplied by the West via Egypt, most of the arms used by the rebels are captured from Soviet or Afghan forces or are locally made copies of the ancient Lee Enfield single-shot rifle.

With their enhanced fire power, the rebel forces appear to be doing well against Afghan and Soviet troops. Twice they all but took over Afghanistan's second largest city, Kandahar, most recently in a two-day fire fight late last month, and they still hold southern enclaves of that battered city.

They have successfully defended the strategic Panjshire Valley, just 50 miles north of Kabul, from Afghan-Soviet attacks.

Despite their apparent ability to hold the Soviet and Afghan forces at bay, the nationalists operating in the hills have failed to achieve unity. It now appears that the rivalries among the dozen or so rebel factions are hampering efforts to win the support of the Afghan villagers still in the country and are preventing tribal bands from capitalizing on each other's military successes.

Even so, perhaps the greatest surprise since the Soviet invasion has been the tenacity of the resistance fighters, who despite their lack of training and equipment continue fighting against Soviet tanks, flame-throwing helicopter gunships and Mig fighters.

While the fighting continues, the Soviet-installed government of Babrak Karmal has failed to win popular backing. Internal feuds between his Parcham faction of the communist People's Democratic Party of Afghanistan and the opposing Khalq wing have intensified since the Soviet takeover. There are increasing rumors that Moscow is seeking a replacement for Babrak who might be more successful in uniting the party and building popular support.

Meanwhile, the Soviets have tightened their grip on the Afghan administrative apparatus and the nation's economy. According to a variety of defectors, important decisions are made by Soviet advisers; courts and schools are being switched from a Western European to a Soviet model, and more and more party loyalists are being sent to the Soviet Union for training.

The belief here is that Moscow would like to turn Afghanistan into a communist state much like Mongolia, completely dominated by the Soviet Union but retaining Kabul's independent status and hence its to vote in such world bodies as the United Nations.

With its isolation from the West, the economy of Afghanistan--already one of the poorest nations in the world--has become more and more entwined with that of the Soviet Union.

Afghan trade with the West has dwindled to almost nothing and has been replaced with commerce with the Soviet Bloc at what emigre Afghan economists say are far less advantageous terms.

The greatest loss to Afghanistan, however, may be its people. The State Department estimates that 2.5 million have fled the country, most to neighboring Pakistan but many into Iran. That amounts to about a fifth of the Afghan people and includes most of the country's small number of educated elite