  In this paper we prove the unique identifiability, module the natural
obstruction, for the Calder\'{o}n problem for quasilinear anisotropic
conductivities in two dimensions from the associated Dirichlet-to-Neumann map.
We reduce the problem to the isotropic case using isothermal coordinates. For
this case, we prove the result by using the method of higher order
linearization and Bukhgeim's CGO solutions.
