  We propose and investigate a large class of models possessing resonance
factorized S-matrices. The associated Casimir energy describes a rich pattern
of renormalization group trajectories related to flows in the coset models
based on the simply laced Lie Algebras. From a simplest resonance S-matrix,
satisfying the ``$\phi^3$-property'', we predict new flows in non-unitary
minimal models.
