Alami won in 1991 at the site of Greg Rusedski the junior competition at Wimbledon, and at the side of John Laffnie de Jager the junior competition of the U.S. Open, he also was the singles in the semifinals of the junior competition, the French Open and the final of the U.S. Open. The previous year, he had become a professional tennis player.
His first final on the ATP World Tour, he reached in 1994 in his hometown of Casablanca, but it lost to Renzo Furlan. The following year he scored his first victory on the ATP Challenger Tour by a final against Jordi Arrese in Tashkent. In 1996, he became the first Moroccan tennis player an ATP tournament when he got the upper hand against Nicklas Kulti in Atlanta. A few months later he celebrated his second and last tournament victory in Palermo. The following year, he won at the side of Julián Alonso his only doubles title on the ATP World Tour. Its highest listing in the tennis world ranking he reached in 2000 with position 25 in the singles and in 1998 with position 130 in doubles.
His best individual result at a Grand Slam tournament was reaching the third round at the Australian Open and the French Open, the best result in the doubles competition was also the third round at the 1998 Australian Open.
Alami played between 1990 and 2002 29 single and 21 double roles for the Moroccan Davis Cup team, its individual balance sheet stood at 20 wins with nine defeats. With the Summer Olympic Games in 1992 and Summer Olympics 2000, he went to Morocco. In 1992, he was forced to retire in his Erstrundenbegegnung against the eventual gold medalist Marc Rosset with the score at 1-1 injured in the sets. In 2000, he reached the quarterfinals, where he was Roger Federer defeated.
After retiring from professional sports, he was tournament director of the Qatar ExxonMobil Open in Doha.