A degeneracy that may occur in the PN solution to the multigroup slowing-down problem reported in part I of this work is studied. The considered degeneracy is of first order, i.e., it connects only two groups in the defined multigroup structure. The singularities caused by the higher-energy group in the particular solution for the lower-energy group are removed by (a) adding to this solution convenient multiples of the PN modes that define the homogeneous solution for the lower-energy group and (b) applying a limiting procedure to the resulting expression. The propagation of the degenerate solutions to other groups below the lower-energy group is also studied. A test problem posed some years ago in the context of the FN method is solved to demonstrate the consistency of the developed degenerate solutions. Numerical results are tabulated for several orders of the approximation and are compared with previously reported FN results.