The transport of monoenergetic neutrons with anisotropic scattering and vacuum boundary conditions is studied in plane systems. First, a simple formal equivalence between the transport equations for a critical and for a time-decaying system is established Then, the stationary transport equation is converted into one in which the scattering kernel is completely isotropic and the resulting equation is solved by using the FN method. Numerical results for the higher order criticality eigenvalues and the corresponding time-dependent ones are tabulated for various scattering parameters and dimensions of the bodies. Some selected results are compared with those already available in the literature. It is shown that the FN method yields results with an accuracy of four to six significant figures over a wide range of scattering parameters Finally we make a few remarks about the behaviour of the criticality and time-eigenvalue spectrum of the neutron transport equation with forward and backward scattering.