Abstract An overview of relative differential cross section (DCS) measurements in the range 30–135° for quasielastic scattering (elastic scattering plus rotational and vibrational excitations) of 4–200 eV positrons by N 2 , O 2 , CO, CO 2 , N 2 O and CH 4 , along with recent measurements for C 2 H 2 and S 6 is reported. For N 2 , O 2 , CO and CH 4 well-defined structure is found in the DCSs below the positronium (Ps) formation thresholds, which becomes washed out as the energy is increased above the Ps formation threshold. N 2 O and CO 2 show the least evidence of structure below (and above) the Ps threshold, while SF 6 exhibits noticeable structure not only below, but also above the Ps threshold. These observations indicate that the Ps formation channel may have an effect on the elastic scattering channel, as does the degree of symmetry of the target system, which is consistent with earlier elastic DCS measurements for the inert gas atoms.