  We use a nonlocal maximum principle to prove the global existence of smooth
solutions for a slightly supercritical surface quasi-geostrophic equation. By
this we mean that the velocity field $u$ is obtained from the active scalar
$\theta$ by a Fourier multiplier with symbol $i k^\perp |k|^{-1} m(k|)$, where
$m$ is a smooth increasing function that grows slower than $\log \log |k|$ as
$|k|\rightarrow \infty$.
