Given a complex surface \( S \), we are interested in the description of an \( C^2 \)- action on \( S \).  It is well-known that this kind of action can be seen as the group of transformations given by the global flows of a pair of commuting complete vector fields. Our goal is to locally describe  such actions  around a fixed point of \( S \). 

This is a joint work with Helena Reis and Julio Rebelo.