l) introduced daughter trajectories in order to account for the cancellation mechanism of singularities in n-N backward scattering. In .order to deduce the existence of the daughter trajectories, they used the kine matical 0 (4) symmetry of the scattering Green's function in the zero energy momentum case. On the mass shell, however, we must consider massless bound states in the unequal-mass case, so that we cannot use the 0 (4) symmetry. In order to study this problem, Domokos 2 ) emyloyed the Bethe-Salpeter equation and inferred that spectra of massless and zero energy-momentum solutions are the same. However, his proof is incomplete, since the vanishing of the Fredholm determinant is necessary but not· sufficient for the existence of massless bound states. In the equal-mass case, it has been shown 3 ) by Nakanishi that there exist no Bethe-Salpeter amplitudes for massless bound states with m = l-l, l- 2, ... and l-l (l~ 1). It has also been inferred that the Green's function has multiple poles at s = 0, s being the total energy-momentum square. On the basis of these observations, we study the connection between the spectra of zero energy-momentum solutions and those of massless ones, using the Bethe-Salpeter equation for two spinless particles interacting through a massive scalar field. The masses of two particles and the scalar field are denoted by m l , m 2, and /1, respectively. An equation for the wave function ¢ (PI) is given,4) in the ladder approximation, by