A spatial adaptive grid method is presented for the solution of two-dimensional neutron transport problems employing the spherical harmonics method within the framework of the variational nodal method. The work represents the generalization of an approach previously applied to the neutron diffusion equation. After reviewing pertinent aspects of the derivation of the variational nodal response matrices, an a posteriori estimator of the local error in the scalar flux is developed. An iterative adaptive procedure is then presented, and application is made to two-dimensional problems. Results are presented for a P5 solution of the well-known Iron-Water Benchmark Problem.