Four series of conjugated oligomers are studied by AMI-CAS-CI method with the purpose to describe the adiabatic lowest one-and two-photon excited states. Polyenes where the lowest singlet is of even parity (S-1 = 2A(g)) serve as test for the accuracy of the approach. Oligomers of p-phenylenevinylene (PVn), p-phenylene (PPn) and p-phenyleneethynylene (PEn) with up to n = 6 aromatic rings are taken as prototypes of luminescent conjugated systems where S-1 is dipole-allowed. One-photon excitation energies (E) are found to follow closely the linear E vs 1/n rule, unlike polyenes where the slope is steeper. The lowest two-photon excited state in PV6, PP6 and PE6 is by at least 0.5 eV higher in energy than the dipole-allowed one. The former bears relation to 2A(g) in polyenes, except for PE where a dipole-forbidden singly excited state approaches 1B(u) faster. Relaxation energies are typically smaller than those in polyenes, and decrease with it. For the one-photon exciton they increase from PE to PV to PP, but fall too short to explain the Stokes' shift in the latter.