  The Horndeski action is the most general one involving a metric and a scalar
field that leads to second order field equations in four dimensions. Being the
natural extension of the well known Scalar-Tensor theories, its structure and
properties are worth analysing along the experience accumulated in the latter
context. Here we argue that disformal transformations play, for the Horndeski
theory, a similar role to that of conformal transformations for Scalar-Tensor
theories a l`a Brans-Dicke. We identify the most general transformation
preserving second order field equations and discuss the issue of viable frames
for this kind of theories, in particular the possibility to cast the action in
the so called Einstein frame. Finally, we investigate the physical equivalence
of such frames and their reciprocal relationship.
