Normalized experimental differential cross sections for scattering angles in the range 20°-85° are presented for elastic scattering and excitation of the fundamental vibration of N2 and CO by electrons with impact energy 20 eV. From three of the four differential cross sections we are able to estimate the integral cross sections. The cross sections for N2 are in good agreement with those of Pavlovic et al. The elastic scattering cross sections are compared to the predictions of the polarized Born approximation using five model potentials (including polarization) which have been previously proposed for N2 or CO. The model of Crawford and Dalgarno is in good agreement with experiment and the model of Sampson and Mjolsness can be put in good agreement by changing an empirical "cutoff parameter" by about 0.5a0. The vibrational excitation of N2 appears to be dominated by resonance scattering, as originally suggested by Favlovic et al. We show that the vibrational excitation of CO also appears to be dominated by resonance scattering.