We have performed a Monte Carlo simulation of the drift of electrons through a mixture of gaseous xenon with the lighter noble gas neon at a total pressure of 1 atm. The electroluminescence characteristics and other transport parameters are investigated as a function of the reduced electric field and composition of the mixture. For Xe-Ne mixtures with 5, 10, 20, 40, 70, 90, and 100% of Xe, we present results for electroluminescence yield and excitation efficiency, average electron energy, electron drift velocity, reduced mobility, reduced diffusion coefficients, and characteristic energies over a range of reduced electric fields which exclude electron multiplication. For the 5% Xe mixture, we also assess the influence of electron multiplication on the electroluminescence yield. The present study of Xe-Ne mixtures was motivated by an interest in using them as a filling for gas proportional scintillation counters in low-energy X-ray applications. In this energy range, the X rays will penetrate further into the detector due to the presence of Ne, and this will lead to an improvement in the collection of primary electrons originating near the detector window and may represent an advantage over the use of pure Xe.