We have investigated computationally the two-photon absorption (2PA) properties of donor-acceptor dipolar chromophores, the conjugated backbones of which contain two five membered heterocyclic groups which may be electron-rich (thiophene-2,5-diyl) and/or electron-deficient (thiazole-2,5-diyl). Quantum-chemical calculations (INDO/MRDCI/S-tensor and Sum-Over-States calculations based on DFT-optmized geometries) indicate that the two-photon cross-sections into the lowest two excited states S-1 and S-2 can be tuned by more than an order of magnitude by varying the nature, order, and in tha case of thiazole, orientation of the heterocycles. Going from one thiazole regioisomer to the other has the strongest impact on the 2PA spectra and can even invert the ratio betwenn the 2PA cross-sections of S-1 and S-2. An essential state-analysis reveals that different channels dominate 2PA into S-1 and S-2. The sensitivity of 2PA into S-1 towards the orientation of the thiazole ring stems from a local modulation on the thiazole ring of the change in state dipole moment upon excitation to S-3 Delta(mu-01.) Wheras the dominant essentail parameter through which the thiazole orientation affeects 2PA into S-2 is the transition dipole moment between S-1 and S-2 mu(12).