  This paper concerns the motion of relativistic strings in the Schwarzschild
space-time. As a general framework, we first analyze the basic equations for
the motion of a p-dimensional extended object in a general enveloping
space-time (N; ~g), which is a given Lorentzian manifold, and then particularly
investigate the interesting properties enjoyed by the equations for the motion
of relativistic strings in the Schwarzschild space-time. Based on this, under
suitable assumptions we prove the global existence of smooth solutions of the
Cauchy problem for the equations for the motion of relativistic strings with
small arc length in the Schwarzschild space-time.
