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{\noindent\LARGE{\bf Hanns Stremnizer}\\[1cm]

\noindent\bf{Need for two vectorlike families in SUSY composite models}}\\

Within the context of a viable and economical SUSY preon model, two
vector--like families $Q_{L,R} = (U,D,N,E)_{L,R}$ and $Q^\prime_{L,R} =
(U^\prime,D^\prime,N^\prime,E^\prime)_{L,R}$ with masses of order 1 TeV, one of
which is a doublet of $SU(2)_L$ and the other a doublet of $SU(2)_R$, have been
predicted to exist together with the three observed chiral families. The
existence of these two vector--like families turns out to be crucial especially
for an explanation of the inter--family mass--hierarchy and therefore for the
SUSY preon model itself.  We  study in detail the
expected masses, mixings and decay modes of the vector--like fermions.
Including QCD renormalization--effects, the masses of the vector--like quarks
are expected to lie in the range of 500 GeV to about 2.5 TeV, while those of
the vector--like leptons are expected to be in the range of 200 GeV to 1
TeV.

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