  We study the phase diagram as function of the number of colours and flavours
of asymptotically free non-supersymmetric theories with matter in higher
dimensional representations of arbitrary SU(N) gauge groups. Since matter in
higher dimensional representations screens more than in the fundamental a
general feature is that a lower number of flavours is needed to achieve a
near-conformal theory. We study the spectrum of the theories near the fixed
point and consider possible applications of our analysis to the dynamical
breaking of the electroweak symmetry.
