  In this paper, we give the strong unique continuation property for a general
two dimensional anisotropic elliptic system with real coefficients in a Gevrey
class under the assumption that the principal symbol of the system has simple
characteristics. The strong unique continuation property is derived by
obtaining some Carleman estimate. The derivation of the Carleman estimate is
based on transforming the system to a larger second order elliptic system with
diagonal principal part which has complex coefficients.
