Quantum mechanical techniques are applied to investigate a family of p-conjugated copolymers: poly(9,9'-dimethylfluorene-alt-thiophene) (PFT), poly(9,9'-dimethylfluorene-alt-thieno[3,2-b]-thiophene) (PFTT), poly(9,9'-dimethylfluorene-alt-bithiophene) (PFT2), and poly(9,9'-dimethylfluorene-alt-alpha,a'-bisthieno[3,2-b]-thiophene) (PFTT2). Linear extrapolation is employed to obtain polymers' properties from oligomer calculations. That is, the HOMO-LUMO gaps (Delta(H)-(L)s), band gaps (E(g)s), ionisation potentials and electron affinities of the copolymers are obtained by plotting the corresponding quantities of the oligomers as a function of the inverse chain length (1/n) and extrapolating them to infinite chain length. The electronic properties of the neutral, positive and negative oligomers are determined using the density functional theory (DFT) at B3LYP/6-31G* approximation. The lowest singlet excitation energies of the oligomers of PFT, PFTT, PFT2, and PFTT2 are also determined with the use of the time-dependent DFT again at B3LYP/6-31G* approximation. Comparisons are made with experimental values when possible.