Starting from 1986, she holds the leading player role in national chess selection. She won the bronze team's medal at the Chess Olympiad in Thessalonica 1988, and the individual bronze medal at the Chess Olympiad in Elista 1998. She won the silver medal at the European Team Chess Championship in Batumi 1999. In Shanghai 2001, Alisa Marić played for six members "Rest of the World team" in an exhibition match against China. In Belgrade 2007, she was awarded the prestigious "St. Sava prize" for the 20 year jubilee as a member of national team. She played first board on ten Chess Olympiads (Dubai 1986, Thessalonica 1988, Novi Sad 1990, Moscow 1994, Yerevan 1996, Elista 1998, Istanbul 2000, Calvià 2004, Torino 2006 and Dresden 2008) and five European Team Championships (Batumi 1999, Leon 2001, Plovdiv 2003, Gothenburg 2005 and Novi Sad 2009). Three times Alisa Marić won European Chess Club Cup with "Agrouniverzal" club from Belgrade.