  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. This paper is devoted to a detailed study of 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.
