  The dynamics with an infrared stable fixed point in the conformal window in
QCD like theories (with a relatively large number of fermion flavors) is
studied. The dependence of masses of colorless bound states on a bare fermion
mass is described. In particular it is shown that in such dynamics, glueballs
are much lighter than bound states composed of fermions, if the value of the
infrared fixed point is not too large. This yields a clear signature for the
conformal window, which is in particular can be useful for lattice computer
simulations of these gauge theories.
