This short paper studies the motion of the poles in the first and the second sheets of the scattering amplitude in the Lee model as the coupling constant g2 changes. It is proved that, with or without the left hand cut, with or without the inelastic cut, the theory does not permit the occurrence of poles in the second sheet representing resonances unless the CDD poles are introduced for the inverse amplitude.When the left hand cut is present and the CDD poles are introduced, a pole representing resonance may slip across the normal cut (near the right threshold) into the first sheet as the coupling constant g2 increases. But before this occurs, another pole slips into the first sheet across the left hand cut (near the left threshold). Motion of poles in the two sheets is plotted for one such special case.When the left hand cut is absent and the CDD poles are not yet introduced, it is pointed out that no passage of poles of one sheet into another sheet is possible so long as g2>0. When the CDD poles are introduced, such passage becomes possible. It is shown that if a pole in the second sheet slips across the normal cut on increasing g2 beyond a certain value g12>0, then before g2 reaches this value, another pole enters the first sheet at-∞. Needless to say, poles entering from the left usually provide ghosts.These general features are believed to hold for field-theoretical models in general.