Two-point correlations of the Gaussian symplectic ensemble from periodic orbits

We determine the asymptotics of the two-point correlation function for quan tum systems with half-integer spin which show chaotic behaviour in the clas sical limit using a method introduced by Bogomolny and Keating. For time-re versal-invariant systems we obtain the leading terms of the two-point corre lation function of the Gaussian symplectic ensemble. Special attention has to be paid to the role of Kramers' degeneracy.