  We develop and analyze an ultraweak formulation of linear PDEs in
nondivergence form where the coefficients satisfy the Cordes condition. Based
on the ultraweak formulation we propose discontinuous Petrov--Galerkin (DPG)
methods. We investigate Fortin operators for the fully discrete schemes and
provide a posteriori estimators for the methods under consideration. Numerical
experiments are presented in the case of uniform and adaptive mesh-refinement.
