We have investigated the acoustic plasma branch present in the longitudinal spectrum of two spatially separated parallel quasi-two-dimensional conducting layers. Our approach is based on the dielectric theory and is completely analytical within the random-phase approximation. By means of a systematic analysis we have obtained several exact results concerning the plasma dispersion relation. In particular, we have derived an exact expression for ${c}_{p}$ the acoustic plasmon group velocity in terms of the effective masses, densities and geometrical parameters of the heterostructure. We find that when the two layers are identical the system always admits a branch of acoustic plasmons as undamped modes for any finite value of the distance between the layers.