  Low-temperature, electronic transport in Landau levels N>1 of a
two-dimensional electron system is strongly anisotropic. At half-filling of
either spin level of each such Landau level the magnetoresistance either
collapses to form a deep minimum or is peaked in a sharp maximum, depending on
the in-plane current direction. Such anisotropies are absent in the N=0 and N=1
Landau level, which are dominated by the states of the fractional quantum Hall
effect. The transport anisotropies may be indicative of a new many particle
state, which forms exclusively in higher Landau levels.
