In this brief paper, the author presents a critical analysis of how LatinAmerican electroacoustic and computer music had evolved over the thirty-year period up to 1998. By contrasting two particular pieces that represent the two stylistic and technological groups under consideration - Homenaje a la Flecha Clavada en el Pecho de Juan Díaz de Solís by Coruín Aharonían (Uruguay) representing pure LatinAmerican contemporary music, and Nahual II by Roberto Morales-Manzanares (Mexico) representing LatinAmerican computer music - he establishes the evolutionary tendencies in compositional approach for these two groups.