  In this paper we construct non-Abelian gauge theories with fermions and
scalars that nevertheless possess asymptotic freedom.The scalars are taken to
be in a chiral multiplet transforming as $(2,2)$ under $SU(2)_L\otimes SU(2)_R$
and transforming as singlets under the colour SU(3) group. We consider two
distinct scenarios, one in which the additional scalars are light and another
in which they are heavier than half the Z-boson mass. It is shown that
asymptotic freedom is obtained without requiring that all additional couplings
keep fixed ratios with each other. It is also shown that both scenarios can not
be ruled out by what are considered standard tests of QCD like R- parameter,
g-2 for muons or deep inelastic phenomena. The light mass scenario is however
ruled out by high precision Z-width data (and only by that one data).The heavy
mass scenario is still viable and is shown to naturally pass the test of
flavour changing neutral currents. It also is not ruled out by precision
electroweak oblique parameters. Many distinctive experimental signatures of
these models are also discussed.
