Results are presented of high-resolution scattering experiments involving electron collisions with CO2 and CS2, between a few meV and 200 meV impact energy. Virtual state scattering is shown to dominate the low-energy behaviour for both species. The most striking features of the scattering spectrum for CS2 are, however, giant resonances with cross sections greater by more than an order of magnitude than those generally encountered in low-energy scattering. A strong feature centred at 15 meV is attributed to the involvement of and is interpreted to be a consequence of the virtual state effect.