The coupled problem for a generalized Newtonian Stokes flow in one domain and a generalized Newtonian Darcy flow in a porous medium is considered in this talk. Both flows are treated as a first order system in a pseudostress-velocity formulation for the Stokes problem and a volumetric flux-hydraulic potential formulation for the Darcy problem. The coupling along an interface is done by using the well known Beavers-Joseph-Saffman interface condition. A least squares finite element method is used for the numerical approximation of the solution. It will be shown that the least squares functional corresponding to the nonlinear first order system is an efficient and reliable error estimator which allows for adaptive refinement. Due to the nonlinearity of the problem a Gauss-Newton method will be used to solve the problem iteratively.