Llosa hails from one of Peru's most influential families; their activities have encompassed politics, the arts, broadcasting and other media. His cousin, Mario Vargas Llosa (author of "Aunt Julia and the Scriptwriter"), is a celebrated practitioner of the "magic realism" movement in literature. The pair collaborated on a weekly investigative news program entitled "The Tower of Babel" (Llosa producing and directing) that was distributed throughout the Spanish-speaking world. The filmmaker adapted his cousin's short story for the feature "Dia Domingo". Llosa also served as campaign manager for Vargas Llosa's failed 1990 presidential bid in Peru.
Llosa's first involvement with the US film industry was as an assistant to producer-director William Friedkin and a dialogue coach on the lavish jungle suspenser "Sorcerer" (1977), shot largely in the Dominican Republic and Mexico. Exploitation guru Roger Corman later "discovered" Llosa and had him produce and/or direct half a dozen Peru-lensed genre flicks under his expansive auspices. These almost straight-to-video releases included the political thriller "Hour of the Assassin" (1987) starring Erik Estrada and Robert Vaughn, the sci-fi actioner "Crime Zone" (1989) with David Carradine and Sherilyn Fenn, and the suspenser "Full Fathom Five" (1990) headlined by Michael Moriarty. Llosa made his American movie breakthrough helming "Sniper" (1993), a middling jungle-set thriller starring Tom Berenger and Billy Zane. He entered the big leagues as the director of "The Specialist" (1994) a pyrotechnical extravaganza featuring what should have been an explosive pairing of Sylvester Stallone and Sharon Stone but which fizzled instead. In 1997, he helmed the critically-derided but box-office hit thriller "Anaconda", set in the Amazon basin.