It was conformed by Garo Arakelián (guitar), Alejandro Spuntone (vocals), Irvin Carballo (drums) and Carlos Ráfols (bass).

La Trampa appeared in scene in 1991 being conformed since winter 1990 by the first two members, architecture students Garo Arakelián and Sergio Schellemberg.

A little time later Nicolás Rodríguez left the band and Daniel “Chino” González took his place, taking charge of the drums for the following years.

It was also in 1995 that Daniel "Chino" Gonzalez left the band taking his place for over one year Javier "Pichu" Villanustre, who got to record "En la noche" a cover of Los Estomagos that was included in "Extrañas Visiones" a tribute album to the band along with some other well known performers such as El Peyote Asesino, Claudio Taddei, Los Traidores, The Supersonicos, Eduardo Darnauchans and more.

That December they stopped performing live in order to start composing for what would be their second studio album called Calaveras ("Skulls"), but they had already gone through another change when 'Pichu' Villanustre left the band without someone to take care of drums.

Calaveras still has its folk influences, but on the contrary to 'Toca y obliga' where that was shown with the music of the bandoneon now it was the drums that took care of those features with rhythms varying from chacarera and malambo to plain rock and roll, but still the milonga and tango were present in their compositions.

The number of fans of the band grew, and by 2001 La Trampa sold out in well-known performing centers like Teatro de Verano and Plaza Mateo.

On 2008, after a long retreat from the stages, La Trampa had a change in their line-up as Alvaro "Alvin" Pintos left to be a full-time member of El Cuarteto De Nos.