  We consider Orlicz--Laplace equation $-div(\frac{\varphi'(|\nabla
u|)}{|\nabla u|}\nabla u)=f$ where $\varphi$ is an Orlicz function and either
$f=0$ or $f\in L^\infty$. We prove local second order regularity results for
the weak solutions $u$ of the Orlicz--Laplace equation. More precisely, we show
that if $\psi$ is another Orlicz function that is close to $\varphi$ in a
suitable sense, then $\frac{\psi'(|\nabla u|)}{|\nabla u|}\nabla u\in
W^{1,2}_{loc}$. This work contributes to the building up of quantitative second
order Sobolev regularity for solutions of nonlinear equations.
