A solvable field-theoretical model is examined with respect to its asymptotic behaviour in strong coupling. The model entails the interaction via Yukawa coupling of a regularized fermion field with a boson field which is spurious,i.e. a boson carrying neither momentum nor energy. The amplitudes in the model are analytic for all finite values of the coupling constant, and their behaviours for asymptotically large coupling are derived. The form of the Green’s functions in the limit is explicitly written with implications on the feasibility of nonperturbative approaches which are perturbative in the strong coupling. This may provide some insights into the question of applicability of field theory to strong interactions.