The notion of uniform circular motion in a general spacetime is introduced as a particular
case of a planar motion. The initial value problem of the corresponding di erential
equation is analysed in detail. Geometrically, an observer which obeys a uniform circular
motion is characterized as a Lorentzian helix. The completeness of its inextensible
trajectories is studied in Generalized Robertson-Walker spacetimes and in a relevant family
of pp-wave spacetimes. The results may be physically interpreted saying that, under
reasonable assumptions, a uniformly circular observer lives forever in these spacetimes,
providing the absence of the singularities de ned by these timelike curves
