  Using mainly tools from [B.13] and [B.15] we give a necessary and sufficient
condition in order that a holomorphic action of a connected complex Lie group
$G$ on a reduced complex space $X$ admits a strongly quasi-proper meromorphic
quotient. We apply this characterization to obtain a result which assert that,
when $G = K.B$ \ with $B$ a closed complex subgroup of $G$ and $K$ a real
compact subgroup of $G$, the existence of a strongly quasi-proper meromorphic
quotient for the $B-$action implies, assuming moreover that there exists a
$G-$invariant Zariski open dense subset in $X$ which is good for the
$B-$action, the existence of a strongly quasi-proper meromorphic quotient for
the $G-$action on $X$.
