  We consider the algebraic curve defined by $y^m = f(x)$ where $m \geq 2$ and
$f(x)$ is a rational function over $\mathbb{F}_q$. We extend the concept of
pure gap to {\bf c}-gap and obtain a criterion to decide when an $s$-tuple is a
{\bf c}-gap at $s$ rational places on the curve. As an application, we obtain
many families of pure gaps at two rational places on curves with many rational
places.
