The dynamical matrix, dielectric response tensor, and dispersion relat
ions for a strongly correlated unmagnetized superlattice are formulate
d in the quasilocalized charge approximation. Analysis of the dispersi
on relations at wavelengths long compared with the spacing d between a
djacent layers indicates that the random-phase-approximation (RPA) col
lective-mode structure is substantially modified by particle correlati
ons. In earlier works [see, e.g., G. Kalman, Y. Ren, and K. I. Golden,
Phys. Rev. B 50, 2031 (1994)] the authors reported the existence of a
long-wavelength energy gap in the acoustic plasmon band generated by
strong interlayer correlations. The present analysis indicates the exi
stence of a gapped shear mode band which is wholly maintained by Coulo
mbic interlayer interactions over and above the RPA. When interlayer i
nteractions are taken into account only through the average RPA field,
the band collapses into a single shear mode which exhibits the long-w
avelength acoustic dispersion characteristic of the correlated two-dim
ensional electron liquid. Other interesting effects include (i) an opt
ical-phonon crystal-like dispersion exhibited by the in-phase plasmon
at long wavelengths for d sufficiently small; and (ii) an acoustic-pho
non dispersion exhibited by the in-phase shear mode at long wavelength
s.