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High-mobility two-dimensional electron systems may be one of the bases of future spintronic devices, where the spin states of ballistic electrons could be manipulated via external gate voltages and the resulting spin-orbit fields. Therefore, the knowledge of spin dynamics in such systems is of technical interest and offers on the other side an exciting view on the underlying physics. Here, we present time-resolved Faraday rotation measurements in a high-mobility two-dimensional electron system in a GaAs/AlGaAs quantum well structure grown along the [001] direction. Even without applied external magnetic fields the optically generated spin ensemble shows a coherent precession about the effective spin-orbit field. If a nonquantizing magnetic field is applied normal to the sample plane, the effective spin-orbit fields are rotated by the cyclotron motion of the electrons. This rotation leads to fast oscillations in the spin polarization about a nonzero value and an strong increase of the spin dephasing times. The measurement data is in excellent agreement with a model based on a kinetic equation approach. [ABSTRACT FROM AUTHOR]