  We investigate the spin dynamics of high-mobility two-dimensional electrons
in GaAs/AlGaAs quantum wells grown along the $[001]$ and $[110]$ directions by
time-resolved Faraday rotation at low temperatures. In measurements on the
$(001)$-grown structures without external magnetic fields, we observe coherent
oscillations of the electron spin polarization about the effective spin-orbit
field. In non-quantizing magnetic fields applied normal to the sample plane,
the cyclotron motion of the electrons rotates the effective spin-orbit field.
This rotation leads to fast oscillations in the spin polarization about a
non-zero value and a strong increase in the spin dephasing time in our
experiments. These two effects are absent in the $(110)$-grown structure due to
the different symmetry of its effective spin-orbit field. The measurements are
in excellent agreement with our theoretical model.
