  We define a model category structure on a slice category of simplicial
spaces, called the "Segal group action" structure whose fibrant-cofibrant
objects may be viewed as representing spaces $X$ with a coherent action of a
given Segal group (i.e. a group-like, reduced Segal space). We show that this
model structure is Quillen equivalent to the projective model structure on
$G$-spaces, $\mathcal{S}^{\mathbb{B}G}$, where $G$ is a simplicial group
represented by this Segal group. Since Segal group actions are invariant under
weak monoidal endofunctors of spaces they enable to construct, for an arbitrary
$G$-space $X$, an "equivariant Postnikov tower" which in degree $n$ has $P_nX$
viewed as a space with a coherent action of (the Segal group corresponding to)
$P_nG$.
