The stochastic acceleration of electrons in lower hybrid (LH) wave packets is investigated in the context of the Earth's auroral ionosphere and magnetosphere. As suggested by rocket and satellite observations, the packets are assumed to contain a broad spectrum of short wavelength LH waves. The interaction of the strongly magnetized electrons with a LH packet occurs mainly in the direction parallel to the background magnetic field, and can in a first approximation be described by a quasi-linear velocity diffusion equation. An analytical expression is derived for the diffusion coefficient and used in Monte-Carlo test-particle calculations. These simulations exhibit the formation of high-energy tails on both sides of the electron parallel velocity distribution. A model is proposed in order to explain the downgoing field-aligned bursts of about 10 eV to 1 keV electrons which are observed by auroral rockets within inverted-V structures at altitudes of several hundreds of kilometers. ¿ American Geophysical Union 1995