  We construct extended technicolor (ETC) models that can produce the large
splitting between the masses of the $t$ and $b$ quarks without necessarily
excessive contributions to the $\rho$ parameter or to neutral flavor-changing
processes. These models make use of two different ETC gauge groups, such that
left- and right-handed components of charge $Q=2/3$ quarks transform under the
same ETC group, while left- and right-handed components of charge -1/3 quarks
and charged leptons transform under different ETC groups. The models thereby
suppress the masses $m_b$ and $m_\tau$ relative to $m_t$, and $m_s$ and $m_\mu$
relative to $m_c$ because the masses of the $Q=-1/3$ quarks and charged leptons
require mixing between the two ETC groups, while the masses of the $Q=2/3$
quarks do not. A related source of the differences between these mass
splittings is the effect of the two hierarchies of breaking scales of the two
ETC groups. We analyze a particular model of this type in some detail. Although
we find that this model tends to suppress the masses of the first two
generations of down-type quarks and charged leptons too much, it gives useful
insights into the properties of theories with more than one ETC group.
