  A general form of multi-channel Bethe-Salpeter equation is considered. In
contradistinction to the hitherto applied approaches, our coupled system of
equations leads to the simultaneous solutions for all relativistic four-point
Green functions (elastic and inelastic) appearing in a given theory. A set of
relations which may be helpful in approximate treatments is given. An example
of extracting useful information from the equations is discussed: we consider
the most general trilinear coupling of N different scalar fields and obtain -
in the ladder approximation - closed expressions for the Regge trajectories and
their couplings to different channels in the vicinity of l = -1. Sum rules and
an example containing non-obvious symmetry are discussed.
