A recent weekend of political violence in which two died and dozens were wounded has convinced many Italians that their country is becoming prone to political violence of the sort that plagues much of South America. Political leaders here are warning that failure to check spiraling disorders could have drastic consequences for Italian democracy.

Two weeks ago, student demonstration in Rome and Bologna turned into riots following the death of a leftist student shot by police in Bologna and the killing of a police officer in Turin.

In Bologna, high school and college students rampaged through the streets of the medieval university quarter, Police used armored vehicles to help clear the are.

In Rome, 14 policemen were wounded by gunfire after a peaceful march by more than 50,000 students from all over Italy was disrupted by extremist bands who fought with police, overturned cars, and attacked the headquarters of the ruling Christian Democratic Party, its newspaper, and a bank.

The disturbance led Interior Minister Francesco Cossiga to condemn what he termed "a preconceived and criminal design of guerrilla warfare" and to warn that "our would-be-'tupamaros' must realize that there is no room for their madness." The Tupamaros were leftist urban guerrillas in Uruguay.

In recent years, Italians have been forced to recognize they live in a country where political ideas increasingly are being expressed in terroristic and violent forms.

Police, who classifly terrorist acts and political disorders separately, point out that since the student-worker disturbance of 1968 and 1969 there has been a steady increase in political violence here from both extremes, left and right.

Last year "terrorist episodes," which can include minor acts like throwing rocks at party headquarters, soared to 1,353, compared to about 170 in 1968 and 702 in 1975.

Political disorders, rare before 1968, began increasing in the early 1970 and now occur at the rate about 20 a day. These include clashes between political factions, primarily in schools, and streetfighting between leftists and rightists.

Terroism in Italy, including the 1969 Milan bombing in Piazza Fontana, in which 16 persons died and 100 were wounded, has taken about 70 lives. Nearly 40 have died in other political disorders.

Many of the victims of terrorism are police and officials. The 12 killed last year in what some police call "a small private war betwen them and us" included two magistrates, two deputy police chiefs and two other policemen.

The number of terrorist groups appears to be growing, along with their incidents.

The murder of Genoa magistrate Francesco Coco was done by the Red Brigades, a group formed in 1970 that began killing in June 1974, specializing in attacks on "fascists, bosses and the police who protect them."

Other leftist terrorists belong to the proletarian Action Nuclei, a group police say has "pure criminal content" and does much of its recruiting among young convicts behind bars for ordinary crimes. Both groups kidnap and rob to raise money.

At the other political extreme, the murder last July of Rome judge Vittorio Occorsio was the work of a rightist group called "New Order," originally an offshoot of the legal neofascis party. This group went underground after being dissolved by court order in November 1973.

Circumstances surrounding the arrest last month of Occorsio's alleged assassin, Pierluigi Concutelli, have led police to suspect that rightist extremists are working increasingly closely with common criminals. Concutelli had in his possession money from a recent kidnaping by a hardened Milan bandit.

Another major rightist terrorist group, Avanguardia Nazionale also went underground in June 1976 after being banned by the courts. The two main rightist groups have organized another 60 smaller units that, officials believe, total no more than 1,000 activists.

There was no indication that any of these terrorist groups were involved in this month's disorders, but eye-witnesses said marauding extremist shouting leftist slogans appeared extremely well-organized and many were armed.

Police say most of Italy's terrorism and political disorders are caused by the far more numerous left, but "a far, extreme left that never includes Communists"

The powerful Italian Communist Party has repeatedly condemned violence and extremism and has been accused by leftist extremists of "selling-out the revolution.

Many of the rightist extremists, about 1,200 of whom were arrested in 1976, belong to the young organization of the neofascist party.

Mounting terrorism and the recent political disorders hav angered police, who have enough trouble dealing with this country's rising crime rate."We are tired of being targets for extremists and of being the only ones involved in maintaining law and order" a veteran police officer said.

"A great many of this country's 80,000 policemen as young men who are anything but right wing.How do you think they feel," he asked "when demonstrating students shout slogans like "If you see something black shoot on sight, its either a fascist or a cop" and 'policeman your place is in the graveyard.'"

The outbreak of violence that kept most Romans and Bolognesi off the streets for two days frightened many Italians into believing that if something is not done soon terroism and disorder will escalate.

The government has pledgd that bills will be pushed through Parliament to help maintain public order by cracking down on the illegal use of arms, speeding up trials, limiting prisoners' leaves and increasing jail personnel.