There are two bands with that name:
1) Rock band formed in 1980. The following year they won the Villa de Oviedo contest and get to publish 3 tracks in a compilation. Their first LP, called Ilegales, appeared in 1982, and since then they've consistently been one of the main Spanish rock bands. 2) Dominican "merenhouse" quartet. Their hits "La Morena", "Fiesta Caliente", "Las Mujeres", "Taqui Taqui", and "La otra" were very popular in all Latin America and in the Hispanic market in the US during the late 90's.

Read more about Ilegales on Last.fm.