  We propose a general construction principle which allows to include an
infinite number of resonance states into a scattering matrix of hyperbolic
type. As a concrete realization of this mechanism we provide new S-matrices
generalizing a class of hyperbolic ones, which are related to a pair of simple
Lie algebras, to the elliptic case. For specific choices of the algebras we
propose elliptic generalizations of affine Toda field theories and the
homogeneous sine-Gordon models. For the generalization of the sinh-Gordon model
we compute explicitly renormalization group scaling functions by means of the
c-theorem and the thermodynamic Bethe ansatz. In particular we identify the
Virasoro central charges of the corresponding ultraviolet conformal field
theories.
