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It is known that Horndeski theories, like many other scalar-tensor gravities,do not support static, spherically symmetric wormholes: they always have eitherghosts or gradient instabilities among parity-even linearized perturbations.Here we address the issue of whether or not this no-go theorem is valid in"beyond Horndeski" theories. We derive, in the latter class of theories, theconditions for the absence of ghost and gradient instabilities fornon-spherical parity even perturbations propagating in the radial direction. Wefind, in agreement with existing arguments, that the proof of the above no-gotheorem does not go through beyond Horndeski. We also obtain conditionsensuring the absence of ghosts and gradient instabilities for all parity oddmodes. We give an example of beyond Horndeski Lagrangian which admits awormhole solution obeying our (incomplete set of) stability conditions. Eventhough our stability analysis is incomplete, as we do not consider sphericallysymmetric parity even modes and parity even perturbations propagating inangular directions, as well as "slow" tachyonic instabilities, our findingsindicate that beyond Horndeski theories may be viable candidates to supporttraversable wormholes.

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