  We consider a family of contour dynamics equations depending on a parameter
$\al$ with $0<\alpha\leq 1$. The vortex patch problem of the 2-D Euler equation
is obtained taking $\alpha\to 0$, and the case $\alpha=1$ corresponds to a
sharp front of the QG equation. We prove local-in-time existence for the family
of equations in Sobolev spaces.
