Alonso appeared in 1994 and 1995 at the Orange Bowl International Championships, the unofficial junior tennis championship in Miami Beach , and reached the quarterfinals. In 1994 he was defeated by Nicolás Lapentti , and the following year by Tommy Haas . In 1996 he became a professional tennis player and won his first title on the ATP World Tour the following year . In singles he won against local hero Marcelo Ríos in Santiago , in doubles he won alongside Karim Alami in Marbella . The following year he won the second and last tournament win in singles and doubles. He also won two more singles and three doubles titles on the ATP Challenger Tour . He reached the highest ranking in the tennis world rankings in 1998 with position 30 in singles and position 53 in doubles.
His best individual result at a Grand Slam tournament was reaching the second round of the Australian Open , which he achieved two years in a row. In the doubles competition he stood alongside Nicolás Lapentti in the quarterfinals of the French Open in 1998 , after they had defeated Ellis Ferreira and Rick Leach , who were fifth in the first round .
Alonso played two singles and three doubles games for the Spanish Davis Cup team between 1998 and 1999 . He won his two singles games, of the three double encounters he gave up two. His greatest success with the team was participation in the semi-finals of the world group in 1998. In the 1: 4 defeat against Sweden he won the only point for Spain by defeating Thomas Johansson .