When news of the continued violence in Miami's black community spread through the city on Wednesday, Gladys Borges' Cuban-American family and friends moved into action.

Her 82-year-old grandfather monitored a Spanish-speaking radio station for any news that the violence in the predominantly black Overtown community was nearing the Veterans Administration hospital a few blocks away where Borges works as a researcher.

Friends from the predominantly Cuban Roman Catholic church Borges attends called her throughout the day to make sure she was all right and keep her abreast of the latest developments.

She left work early Wednesday at the urging of her family and friends who heard reports that Overtown residents were throwing rocks and bottles at cars--particularly those carrying white passengers--on the expressway Borges uses to get home.

Even though the disturbance was virtually over today, Borges' fiance insisted on driving her to work and home as a precaution.

Reaction in the Borges family was typical of fear caused in Miami's Latino community by the violence in black neighborhoods. It is a fear that Cuban leaders said today is threatening to unravel a tenuous peace between blacks and Latinos here since the 1980 riots in the predominantly black residential area of Liberty City north of Overtown.

They said the situation will not be helped by the fact that the Overtown disturbance was triggered by the shooting of a 20-year-old black man by a Hispanic police officer.

"Yes there will be some friction. Some people will look at it as we Cubans being responsible," said Jose Feito, an architect and a member of the board of directors of the Greater Miami Chamber of Commerce. "But I think we blacks and Cubans will be able to keep on working together."

Blacks and Latinos, who make up about 75 percent of Miami's population, live in virtually segregated communities. But since 1980 when both the riots and the arrival of some 125,000 Cuban refugees threatened to divide this city against itself, city and community leaders have tried to promote greater understanding between blacks, Latinos, and Anglos.

Miami United, a private group, was formed to promote better "tri-ethnic" relations and to seek solutions to the city's social and economic problems. Blacks, whites and Hispanics on the Chamber of Commerce together raised about $7 million for the economic development of the Liberty City area. And the Cuban National Planning Council has been working to bring together Cuban contractors with black businessmen to work on development projects in the black areas.

"I think this renewed violence is going to hurt," said Wilfredo Gort, executive director of the Downtown Miami Business Association.

But Gort noted that while the Cuban leadership kept out of the negotiations during the 1980 riots and many Cuban residents reacted by arming themselves, a Cuban member of Miami United, Eduardo Padrone, this time appeared on television along with black community leaders to urge Overtown residents to remain calm.

But in the streets of Little Havana, a neighborhood of Cuban-owned small businesses, there was little sympathy for the actions this week of some Overtown residents.

"I'm not prejudiced but it seems like those people just took advantage of a situation," said Jose Garcia, who works in silk screening. "Isn't it worse when you start to burn up cars and throw rocks? Just more people get hurt and don't they realize there's a lot of Latin people being killed by the police too?"

"You have an ideological problem between Cubans and blacks that is neither racial nor cultural," said Xavier Suarez, a former candidate for city commissioner who toured the streets of Overtown today with officials.

"It's just that the majority of Cubans happen to be conservative. The Cubans would want someone, like the police or the National Guard, to go in there and quell the violence right away. Of course, a lot of Anglos felt the same way."