As separate squads, neither of the Koreas had been able to beat the team they called the "Great Wall" of table tennis: China, winner of eight consecutive women's world team titles leading up to that year's championships in Chiba, Japan. But Hyun, a 20-year-old from the southern port city of Busan, and the baby-faced 22-year-old Li teamed to help the Koreas finally break China's streak and clinch the gold medal.
The recent South Korean film "As One" reconstructs the complex bid to field a united team of players from both sides of the world's most heavily militarized border. It was just four years after North Korean agents blew up a South Korean airliner, killing all 115 people on board.
At first, the players regarded one another suspiciously. Their countries had fought against one another for three years in the 1950s, and the Korean Peninsula has remained in a state of war since a truce was signed in 1953. In the film, trash talking at a team banquet leads to a brawl.
"Did you see their faces?" one South Korean athlete says in the film. "So morbid."
In a telephone interview with AP, Hyun recalled her dismay when she learned she would be playing doubles with Li, whom she considered a notch lower in skill.
"I was too young to understand how symbolic it was," she said.
Both players were fiercely competitive. Getting past their rivalry, as well the cultural clashes, took time. The film contrasts the rigid orderliness of the North Koreans with the constant horseplay among the southerners.
Then, one day, Li missed practice, debilitated by hepatitis.
"My heart ached," Hyun said. "Aside from the rivalry between us and between our countries, I started hoping Li would get better and do well for her country."
Against all odds, friendships blossomed. The once-reluctant teammates together sang ballads that predated the peninsula's division. Their coaches bonded in a marathon drinking session. Stiff handshakes became high fives.
Li and Hyun developed a profound respect and affection for one another. They became confidantes as well as teammates, and their performances were crucial in helping the unified team win the women's title.
A 1991 photo shows the two in identical blue team suits, smiling, their hands clasped.
"We speak the same language," Li said. "We're the same people. We're Korean. We all had the same goal: To win."
But as the movie shows, they sometimes sparred teasingly with their ping pong paddles as well as with words.
Did you ever want to live in the South?" says the actress, Ha Ji-won, who portrays Hyun. "We live better than the North. The health care is better."
"Isn't life better in the U.S. than the South?" the fictional Li, played by Bae Doona, fires back. "Why don't you live there?"
In the film, Li admires Hyun's gold ring. Hyun confides that it was a gift from her father, who was hospitalized back home.
At their tearful parting, Hyun presses the ring into Li's hands.
Afterward, the two went home to their opposing sides of the Demilitarized Zone.
Restricted from writing or phoning, they saw each other only one more time, at the next world championships, when the two Koreas competed separately and Hyun won the singles titles. China resumed its dominance in the women's team event and launched another winning streak following the solitary triumph of the united Korean team.
In the years that followed, expectations were high that the two Koreas would keep using sports diplomacy to forge peace at least on the playing field. And at times, there was some traction.
In 2000, North and South Korean athletes marched together into the opening ceremony of the Sydney Olympics under the unified Korea flag, sparking a standing ovation. Months earlier, their leaders held a landmark summit in Pyongyang, raising hopes of reconciliation. There was talk during those "sunshine" years of suiting up as a combined team for competition again.
But with relations now at their lowest point in decades, and Pyongyang issuing regular threats against South Korean President Lee Myung-bak and his allies, that won't happen in London.
Team Korea, which is sending 245 South Koreans to the London Olympics to compete in 22 sports, will keep its distance from Team PRK Korea, which is sending 51 athletes to compete in nine sports, including women's football, boxing and, of course, table tennis.
Pyongyang also will send its first delegation to the Paralympics headed by none other than Li.
At 44, she is still athletic and has devoted herself to bringing the disabled out of the shadows of North Korean society through sports. Li, whose son has cerebral palsy, now heads her country's first Paralympic committee and was interviewed at the Taedonggang Cultural Center for the Disabled in Pyongyang.
Hyun went on to become one of South Korea's most decorated players and respected coaches, an Olympic gold medalist who in 2010 was inducted into the International Table Tennis Federation's Hall of Fame. Now 42, she is a director of the Korea Table Tennis Association in Seoul.
She misses Li, and remembers nights spent huddled together over snacks, away from the watchful eye of the North Korean security detail. An attempt by the filmmakers to bring them together for a reunion in Beijing was thwarted when South Korea's Unification Ministry denied Hyun's request for permission to meet the North Korean.
Were they ever to meet again, Hyun said, she would tell Li all about her family.
Nor have the ensuing two decades diminished Li's affection for Hyun, who she describes as "a woman of few words" straightforward and ambitious.
"I miss her very much," said Li, her eyes glistening with tears. She still, 21 years later, cherishes the gold ring given to her by her old doubles partner.