  The spectra of invertible weighted composition operators $uC_\varphi$ on the
Bloch and Dirichlet spaces are studied. In the Bloch case we obtain a complete
description of the spectrum when $\varphi$ is a parabolic or elliptic
automorphism of the unit disc. In the case of a hyperbolic automorphism
$\varphi$, exact expressions for the spectral radii of invertible weighted
composition operators acting on the Bloch and Dirichlet spaces are derived.
