  We describe a generalisation of the well known Pancharatnam geometric phase
formula for two level systems, to evolution of a three-level system along a
geodesic triangle in state space. This is achieved by using a recently
developed generalisation of the Poincare sphere method, to represent pure
states of a three-level quantum system in a convenient geometrical manner. The
construction depends on the properties of the group $SU(3)\/$ and its
generators in the defining representation, and uses geometrical objects and
operations in an eight dimensional real Euclidean space. Implications for an
n-level system are also discussed.
