  The conductivity of a two-dimensional electron gas in a parallel magnetic
field is calculated. We take into account the magnetic field induced
spin-splitting, which changes the density of states, the Fermi momentum and the
screening behavior of the electron gas. For impurity scattering we predict a
positive magnetoresistance for low electron density and a negative
magnetoresistance for high electron density. The theory is in qualitative
agreement with recent experimental results found for Si inversion layers and Si
quantum wells.
