Abstract
The impossibility of composite models of two or more generations of quarks and leptons is shown using preons with strong $\mathrm{S}{\mathrm{U}}_{C}(3)$ quantum numbers and either the electroweak $\mathrm{S}{\mathrm{U}}_{L}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ or $\mathrm{S}{\mathrm{U}}_{L}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{S}{\mathrm{U}}_{R}(2)\ifmmode\times\else\texttimes\fi{}{\mathrm{U}}_{B\ensuremath{-}L}(1)$ quantum numbers. The preon models considered are the simplest: $\mathrm{FFF}$ and $\mathrm{FB}$ ($F$ is fermion and $B$ is boson). The constraints imposed on the models are the absence of exotics and anomalies in the strong and electroweak sectors.
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