  In this paper (second in the series) we study the properties of tree-level
binary amplitudes of the infinite-component effective field theory of strong
interaction obeying the requirements of quark-hadron duality and maximal
analyticity. In contrast to the previous paper, here we derive the results
following from less restrictive --- Regge-like --- boundedness conditions. We
develop the technique of Cauchy's forms in two variables and show the
string-like structure of a theory. Next, we derive the full set of bootstrap
constraints for the resonance parameters in (\pi,K) system. Numerical test
shows: (1) those constraints are consistent with data on well established
vector resonances; (2) two light broad resonances -- sigma- and kappa-mesons --
are needed to saturate sum rules following from Chiral symmetry and
analyticity. As a by-product we obtain expressions for the parameters of Chiral
expansions and give corresponding estimates.
