A year after it was shaken by the bloodiest riots ever seen in Yugoslavia, the ethnic Albanian province of Kosovo remains a major problem for president Tito's successors and a touchstone of their ability to hold the country together after his death.

This peculiar-looking provincial capital, where architecturally extravagant buildings jar with the obvious poverty of many of the 70,000 inhabitants, shows few outward signs of the disturbances that erupted here in March and April 1981. Following the riots, in which at least 10 people were killed, a state of emergency was declared in Kosovo. Hundreds of students and workers were arrested, and several local Communist Party leaders were purged after being accused of turning a blind eye to Albanian nationalism.

The state of emergency has been lifted and the university, which was the flash point of much of the unrest, now seems calm. The anti-Yugoslav slogans of the young Albanian demonstrators have been rubbed off the walls and the broken windows of shops and apartment buildings in the city center have been repaired.

The calm, however, is superficial. Even Yugoslav officials agree that the causes of the explosion in Kosovo--the economic backwardness of the province, the historic rivalry between the Albanian and Serbian populations and the frustrations felt by half-educated university students who have little prospect of finding jobs--have not been eradicated.

Last month new disturbances occurred in Pristina when chanting students marched on the city center. On April 3, the first anniversary of the declaration of the state of emergency, nationalist protests flared in the town of Urosevac, 25 miles to the south. Both demonstrations were broken up by riot police and, according to official accounts, 133 people were arrested.

Overshadowed by the dramatic developments in Poland, the unrest last year in Kosovo received relatively little attention from the Western press. Yet, coming just a year after Tito's death, it severely jolted Yugoslavia and illustrated some of the structural weaknesses of this federation of Balkan nations that he ruled for 35 years.

The head of the local television station, Agim Zatriqi, an intensely pro-Yugoslav Albanian, said, "What happened here was like an earthquake. It worried people all over Yugoslavia, particularly since we thought we had settled the national question under president Tito."

The main demand of the demonstrators was that Kosovo, which is about half the size of Maryland, be upgraded from an autonomous province of Serbia to Yugoslavia's seventh constituent republic. The demand was rejected by Yugoslav leaders, who saw it as a step toward Kosovo's secession from Yugoslavia and its unification with neighboring Albania.

Describing the riots in Kosovo as an attempt at "counterrevolution," Zatriqi said: "The enemy thought that the period after Tito's death gave them their best chance for action. Without Tito, they thought they would be successful. Their analysis was not realistic, but certainly they caused us a lot of trouble."

For an outsider, it is difficult to understand why a significant portion of Yugoslavia's 1.7 million ethnic Albanians should be attracted to Albania's Stalinist government. Albanian leader Enver Hoxha, who calls himself a disciple of the late Soviet dictator Joseph Stalin, presides over what is certainly the most isolated and probably the most politically repressive society in Europe. Poor as they are, Yugoslav Albanians are undoubtedly materially better off than their cousins across the mountains in Albania.

The explanation lies partly in the potency of Albanian nationalism, partly in the failure of a costly development strategy for Kosovo that consisted largely of pouring money into the province without controlling how it was spent.

The Albanians, said to be descended from the ancient Illyrians, kept their national identity intact despite centuries of foreign occupation. Hoxha, in World War II, led a Communist uprising against the Italians, who had annexed Albania in 1939. Hoxha then pursued a foreign policy similar in many ways to that of Albania's feudal rulers before him. To preserve his country's independence, he switched allegiances from one patron to another: first Yugoslavia, then the Soviet Union, and finally China.

Culturally, the Albanians have little in common with the Slavic races who account for more than 85 percent of Yugoslavia's 22.5 million population. They speak a separate language that bears no resemblance to those of other Yugoslavs and have their own elaborate codes of honor, including the blood feud or vendetta.

Complicating the problem is the emotional attachment that the Serbs, Yugoslavia's largest national group, always have felt for Kosovo. Today the province is 77 percent Albanian, but historically it was the cradle of Serbia's medieval empire. Every Serbian child is brought up on the heroic tale of how their Prince Lazar was killed fighting the Turks on a Kosovo field in 1389.

The Serbian historical heritage lives on in the magnificent Orthodox monasteries dotted around Kosovo, their walls covered by frescoes of medieval saints and kings.

For two decades after World War II, Kosovo was run by the Serbian minority. This ended with the fall of Alexander Rankovic, Tito's hard-line Serbian police chief in 1966, and widespread riots among Albanians in 1968. The federal government then embarked on a policy of granting Kosovo autonomy and trying to promote its economic development.

Unfortunately, much of the money was misspent on unprofitable industrial projects or grandiose buildings in Pristina such as the university library--a glass-and-marble palace.

During te 1970s, the Yugoslav leadership encouraged Kosovo to develop ties with Albania in an apparent attempt to limit conflict with its prickly neighbor. Albanian books and pamphlets poured into the province and numerous cultural delegations were exchanged. Outside Kosovo, few people paid much attention.

Within Kosovo, however, Hoxha's egalitarian propaganda found fertile ground. With annual incomes averaging $800--one sixth the level of more developed Yugoslav republics such as Slovenia--many Albanians felt discriminated against. "Down with the red bourgeoisie" was one of the slogans chanted by the demonstrators last year.

Nationalist ideas spread particularly strongly at Pristina University. Just 12 years old, it is already one of the largest in the country with 30,000 students, many of them enrolled in the humanities. But while Kosovo is desperately short of qualified experts, many young Albanians cannot find work after leaving college.

Throughout the Tito era, Kosovo's political leadership prevented the Yugoslav press from writing about the stirrings of nationalism in the province and the mass exodus of Serbs and Montenegrins. Only recently was it revealed that 57,000 Serbs and Montenegrins left Kosovo between 1971 and 1981--over a fourth of the total Slav population. Thousands more are believed to have left after last year's riots.

Press restrictions have ended, and Belgrade newspapers are now carrying lurid accounts of Serbian families fleeing Kosovo after allegedly receiving death threats. Magazines have carried pictures of Serbian monasteries being guarded by nuns with rifles.

Many Yugoslavs confess that they see little hope of any short-term solution to the problem. Order has been reimposed through rigorous security measures and all cultural links with Albania have been cut.

In the long term, Tito's successors say they will maintain tighter controls over Kosovo and will not give in to nationalism. Other republics have promised to send an additional $4 billion to the province during the next five years and to keep a closer watch on how it is spent. Political and ideological education of young people is being stepped up.