  We study the long-time existence and behavior for a class of anisotropic
non-homogeneous Gauss curvature flows whose stationary solutions, if exist,
solve the regular Orlicz-Minkowski problems. As an application, we obtain old
and new results for the regular even Orlicz-Minkowski problems; the
corresponding $L_p$ version is the even $L_p$-Minkowski problem for $p>-n-1$.
Moreover, employing a parabolic approximation method, we give new proofs of
some of the existence results for the general Orlicz-Minkowski problems; the
$L_p$ versions are the even $L_p$-Minkowski problem for $p>0$ and the
$L_p$-Minkowski problem for $p>1$. In the final section, we use a curvature
flow with no global term to solve a class of $L_p$-Christoffel-Minkowski type
problems.
