  We develop a method of computing the excited state energies in Integrable
Quantum Field Theories (IQFT) in finite geometry, with spatial coordinate
compactified on a circle of circumference R. The IQFT ``commuting
transfer-matrices'' introduced by us (BLZ) for Conformal Field Theories (CFT)
are generalized to non-conformal IQFT obtained by perturbing CFT with the
operator $\Phi_{1,3}$. We study the models in which the fusion relations for
these ``transfer-matrices'' truncate and provide closed integral equations
which generalize the equations of Thermodynamic Bethe Ansatz to excited states.
The explicit calculations are done for the first excited state in the ``Scaling
Lee-Yang Model''.
