Double-gamma vibrations in deformed nuclei are analyzed in the context of t
he interacting boson model. A simple extension of the original version of t
he model towards higher-order interactions is required to explain the obser
ved 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 transitio
ns of the highly gamma -anharmonic nuclei Dy-164, Er-166, and Er-168 are in
terpreted in this approach.