  Double-$\gamma$ vibrations in deformed nuclei are analyzed in the context of
the interacting boson model. A simple extension of the original version of the
model towards higher-order interactions is required to explain the observed
anharmonicities of nuclear vibrations. The influence of three- and four-body
interactions on the moments of inertia of ground- and $\gamma$-bands, and on
the relative position of single-$\gamma$ and double-$\gamma$ bands is studied
in detail. As an example of a realistic calculation, spectra and transitions of
the highly $\gamma$-anharmonic nuclei $^{164}$Dy, $^{166}$Er, and $^{168}$Er
are interpreted in this approach.
