Since her arrival in Miami two years ago, Albita has been mesmerizing nostalgic exiles, curious gringos and more than a few celebrities with the traditional country tunes and African rhythms of prerevolutionary Cuba. Madonna, Liza Minnelli, Cindy Crawford, Scan Connery and Gianni Versace have all flocked to Centro Vasco to see the woman who’s resurrected the old sounds while creating new arrangements with elements of rock and jazz. Critics have dubbed her the Latin k. d. lang, but it remains to be seen if Albita’s high-powered friends can help her cross over to the Anglo market. One thing’s for certain: “There is a major buzz about her,” according to Bruno del Granado, a vice president of MTV Latino, which broadcasts in more than a dozen U.S. cities. The buzz grew even louder last month when big-name producer Emilio Estefan Jr. released her new album, “No Se Parece A Nada” (Unlike Anything Else).

Already, Albita was something of a musical phenomenon in her homeland as well as in Europe and Latin America. She grew up in Havana, the daughter of well-known country-music performers, and by 19 was singing and playing her guitar on the Cu-ban-television equivalent of “Hee Haw.” But her friends were too busy jamming to Black Sabbath, Chicago and the Beatles to take her music very seriously. “I was well known, but I wouldn’t say I was popular,” says Albita, who clung stubbornly to the retro sound and formed a band with several musicians who shared her passion. The Cuban government allowed the group to move to Colombia for five years, Albita says, but wanted them to perform for Communist causes and took a part of their earnings. While pretending to visit a Mexican recording studio, they crossed into the United States. “It really upset me that everyone had to leave the country to develop their art, even people who had no interest in politics,” says Albita. “When was he [Castro] going to leave?”

Albita likes to say that the last two years have unfolded like a dream. Sure, the big record labels scoffed at first at the idea of a female Cuban vocalist who wanted to sing old-fashioned country music. But then one night Emilio and Gloria Estefan paid a visit to Centro Vasco. “The minute I heard her, I said, ‘What a voice!’” said Emilio, who, aside from his wife, has produced superstar Jon Secada and the Grammy-winning mambo king Israel (Cachao) Lopez. He signed her soon after that.

Before long, celebrities like Madonna were begging her to perform at private parties. “She completely blew my mind,” says Madonna, who changed the date of her birthday bash last fall when it conflicted with another Albita gig. “She was so authentic.” Madonna’s brother, Christopher Ciccone, directed Albita’s first video to “Que Manera de Quererte” (What a Way of Loving You), a dance number on her new CD that was also on the soundtrack of the movie “The Specialist.” “All this attention is wonderful, but I still don’t believe it,” says Albita. “I think they’re crazy.”

Crazy or not, the true test of Albita’s success will now depend on record sales. Earlier this month, the title track of “No Se Parece” debuted at number 48 on Billboard’s hot dance singles chart, just behind Tupac’s and Paula Abdul’s new releases. Estefan plans to showcase Albita at clubs from New York to Los Angeles. Despite the language barrier, he believes she can appeal to both Latinos and Anglos. But in any case, he argues, the 25 million Latinos who call this country home could easily make Albita a superstar.