We continue our investigation into the theory of coupled πNN-NN systems in succession of an earlier work, in which practical equations and unitarity have been established for all the pertinent amplitudes. First, the equivalence of our theory with that of Mizutani and Koltun is proved. Then, the question of whether theories which adopt the bound-state picture are appropriate for the description of systems of pions and nucleons is carefully discussed. We also show how the equations should be modified when we include the non-pole contribution to the πN P11 channel. Finally, we extend our equations to include relativity and show how to arrive at numerically solvable equations, with relativistic invariance guaranteed. In the NN sector, these equations contain the two time orderings of the OPEP in a correct manner.