Binary mixtures of methanol (CH₃OH) and carbon monoxide (CO) ices were irradiated at 10 K with energetic electrons to mimic the energy transfer processes that occur in the track of the trajectories of MeV cosmic-ray particles. The formation of glycolaldehyde (HCOCH₂OH) was established through the appearance of new bands in the infrared spectrum at 1757, 1700, 1690, 1367, 1267, and 1067 cm^-1. A second C₂H₄O₂ isomer, methyl formate (HCOOCH₃), was also identified by absorptions appearing at 1718, 1159, and 914 cm^-1. Mass spectrometer signals during the warm-up of the ice sample showed sublimation of both the glycolaldehyde and methyl formate; these species were monitored via the C₂H₄O₂⁺ molecular ion at mass-to-charge ratio, m/e, of 60 originating from both glycolaldehyde and the methyl formate isomer. The latter was distinguishable by the presence of a second signal at m/e = 45, i.e., the HCO₂⁺ ion. Kinetic fits of the column densities of the reactants and products suggest the initial step of the formation process is the cleavage of a C–H bond in the methanol molecule to generate either the hydroxymethyl (CH₂OH) or methoxy (CH₃O) radical plus atomic hydrogen. The hydrogen atom holds excess kinetic energy, allowing it to overcome entrance barriers required; therefore, a hydrogen could add to a CO molecule, generating the formyl radical (HCO). This can recombine with the hydroxymethyl radical to form glycolaldehyde or with the methoxy radical to yield methyl formate. Similar processes are expected to form glycolaldehyde and methyl formate in the interstellar medium on grains and possibly on cometary ices, thus providing alternatives to gas-phase processes for the generation of complex species whose fractional abundances compared with H₂ of typically a few times 10^-9 cannot be accounted for solely by gas-phase chemistry.