Low-energy electron impact (E(i) = 0-17 eV) on organic monolayers chemically bound to Au substrates is shown to induce the desorption of H-2. The threshold and the maximum yields for this excitation/reaction/desorption channel are observed at E(i) = 7.0 +/- 0.5 eV and E(i) = 10.0 +/- 0.5 eV, respectively, for each of the n-alkane monolayers examined (Au-S-(CH2)(n)CH3, n = 3, 7, 11, and 15). From the dependence of the H-2 yields on the incident electron energy in the E(i) = 6-12 eV regime, which closely resemble the H- desorption yield previously reported for physisorbed alkanes, we propose that most of the H-2 production originates from the dissociative electron attachment to the n-alkane film constituents; H-2 formation may also proceed by direct excitation of the hydrocarbons to the dissociative S-1 state. The desorption of H-2 from chemisorbed Au-S-CH2C6H5 is first observed at E(i) similar to 7.5 +/- 0.5 eV, with a broad maximum desorption yield extending from E(i) = 12-17 eV. The sensitivity of the desorption yields to the film constituents suggests that H-2 formation proceeds by molecule-specific channels and suggests that chemisorbing volatile species to conductive substrates may be useful in the study of electron-induced reactions of adsorbates at ambient or elevated temperatures. It also indicates that the use of electron beams to prepare reactive surfaces will require detailed characterization studies and highly selective excitation mechanisms to avoid undesirable decomposition channels.