The vacuum emission technique has been used to study electron transport and heating in silicon nitride and silicon oxynitride. The experimental results are compared to data for silicon dioxide in which all the conduction-band electrons can gain several eV of energy at electric fields greater than 2 MV/cm. Although average electron energy as a function of electric field curves are very similar to silicon dioxide, the total number of electrons which can be heated to energies greater than 2 eV is greatly reduced because of the increased trapping in these films. Reduction in hot electrons due to increased trapping is correlated to increasing nitrogen content through the oxynitride phases to silicon nitride. Trapping/detrapping on energetically shallow sites in the forbidden gap controls the bulk limited conduction in these films, and very few electrons are allowed to move freely in the conduction band.