  We propose a covariant entropy bound in gravitational theories beyond general
relativity (GR), using Wald-Jacobson-Myers entropy instead of
Bekenstein-Hawking entropy. We first extend the proof of the bound known in
4-dimensional GR to D-dimensional GR, f(R) gravity and canonical scalar-tensor
theory. We then consider Einstein-Gauss-Bonnet (EGB) gravity as a more
non-trivial example and, under a set of reasonable assumptions, prove the bound
in the GR branch of spherically symmetric configurations. As a corollary, it is
shown that under the null and dominant energy conditions, the generalized
second law holds in the GR branch of spherically symmetric configurations of
EGB gravity at the fully nonlinear level.
