  We derive the effective equations of the membranes dual to black holes in a
particular theory of higher derivative gravity namely Einstein-Gauss-Bonnet
(EGB) gravity at sub-leading order in $1/D$ upto linear order in the
Gauss-Bonnet (GB) parameter $\beta$. We find an expression for an entropy
current which satisfies a local version of second law onshell in this regime.
We also derive the membrane equations upto leading order in $1/D$ but
non-perturbatively in $\beta$ for EGB gravity. In this regime we write down an
expression for a world-volume stress tensor of the membrane and also work out
the effective membrane equation for stationary black holes.
