  We consider the rough differential equation $dY=f(Y)d\bm \om$ where $\bm
\om=(\omega,\bbomega)$ is a rough path defined by a Brownian motion $\omega$ on
$\RR^m$. Under the usual regularity assumption on $f$, namely $f\in C^3_b
(\RR^d, \RR^{d\times m})$, the rough differential equation has a unique
solution that defines a random dynamical system $\phi_0$. On the other hand, we
also consider an ordinary random differential equation
$dY_\delta=f(Y_\delta)d\omega_\de$, where $\omega_\de$ is a random process with
stationary increments and continuously differentiable paths that approximates
$\omega$. The latter differential equation generates a random dynamical system
$\phi_\delta$ as well. We show the convergence of the random dynamical system
$\phi_\delta$ to $\phi_0$ for $\delta\to 0$ in H\"older norm.
