  We prove that Schr\"odinger operators with meromorphic potentials
$(H_{\alpha,\theta}u)_n=u_{n+1}+u_{n-1}+
\frac{g(\theta+n\alpha)}{f(\theta+n\alpha)} u_n$ have purely singular
continuous spectrum on the set $\{E: L(E)<\delta{(\alpha,\theta)}\}$, where
$\delta$ is an explicit function, and $L$ is the Lyapunov exponent. This
extends results of Jitomirskaya and Liu for the Maryland model and of Avila,
You and Zhou for the almost Mathieu operator, to the general family of
meromorphic potentials.
