  By studying the linearization of contour dynamics equation and using implicit
function theorem, we prove the existence of co-rotating and travelling global
solutions for the gSQG equation, which extends the result of Hmidi and Mateu
\cite{HM} to $\alpha\in[1,2)$. Moreover, we prove the $C^\infty$ regularity of
vortices boundary, and show the convexity of each vortices component.
