In the series of the layered highT_c superconductors (A)_1,2 B₂Ca_n−1Cu_nO_2n+3,4 (A=Tl or Bi;B=Ba or Sr), withn=number of consecutive Cu-O layers, the electron energy states of some of the Tl-based systems have been investigated. The electron and phonon dispersion curves have been obtained. The electronic states near the Fermi level are dominated by the hybridized Cu(d) and the O(p) orbitals. The dispersion curves are highly two-dimensional with very small dispersion alongc-axis. The number of bands is enhanced with increase in the number of the consecutive Cu-O planes (n). The present results agree with those obtained earlier for other superconducting phases. The phonons are overall dominated by the vibrations of the light mass oxygen atom modes both lying in or outside the Cu-O planes. The low-frequency phonons involve the motions of the heavier Tl, Ba atoms etc.