  We construct wormholes in Einstein-scalar-Gauss-Bonnet theories with a
potential for the scalar field that includes a mass term and self-interaction
terms. By varying the Gauss-Bonnet coupling constant we delimit the domain of
existence of wormholes in these theories. The presence of the self-interaction
enlarges the domain of existence significantly. There arise wormholes with a
single throat and wormholes with an equator and a double throat. We determine
the physical properties of these wormholes including their mass, their size and
their geometry.
