  As a first step towards a comprehensive investigation of stellar motions
within globular clusters, we present here the results of a study of stellar
orbits in a mildly triaxial globular cluster that follows a circular orbit
inside a galaxy. The stellar orbits were classified using the frequency
analysis code of Carpintero and Aguilar and, as a check, the Liapunov
characteristic exponents were also computed in some cases.
  The orbit families were obtained using different start spaces. Chaotic orbits
turn out to be very common and while, as could be expected, they are
particularly abundant in the outer parts of the cluster, they are still
significant in the innermost regions. Their relevance for the structure of the
cluster is discussed.
