  The full complex phase structure of the meson-baryon reaction amplitude in
coupled channels approach is investigated, including also the photon-baryon
channel. The result may be viewed as a generalization of the well-known
Watson's theorem. Furthermore, the complex phase structure is exhibited for the
pole and nonpole parts of the reaction amplitude in such a way that it will
serve as a convenient common starting point for constructing models with
different levels of approximation, in particular, for building isobar models
where the basic properties of the $S$-matrix can be maintained. Such models
should be useful, especially, in coupled multichannel calculations, where a
large amount of experimental data are considered in resonance analyses, a
situation encountered in modern baryon spectroscopy. In particular, it is shown
that the unitarity of the pole part of the $T$-matrix arises automatically from
the dressing mechanism inherent in the basic scattering equation. This implies
that no separate conditions are required for making this part of the resonance
amplitude unitary as it has been done in some of the existing isobar models.
