  For any field $\Bbb F$ and positive integers $m,n,d$ with $(m,n)\not= (1,1)$,
Farb and Wolfson defined the certain affine varieties ${\rm Poly}^{d,m}_n(\Bbb
F)$ as generalizations of spaces first studied by Arnold, Vassiliev, Segal and
others. As a natural generalization of this, for each fan $\Sigma$ and
$r$-tuple $D=(d_1,\cdots ,d_r)$ of positive integers, the current authors
defined spaces ${\rm Poly}^{D,\Sigma}_n(\Bbb F)$, where $r$ is the number of
one dimensional cones in $\Sigma$. These spaces can also be regarded as
generalizations of the space ${\rm Hol}^*_D(S^2,X_\Sigma)$ of based rational
curves from the Riemann sphere $S^2$ to the toric variety $X_\Sigma$ of degree
$D$, where $X_\Sigma$ denotes the toric variety (over $\Bbb C$) corresponding
to the fan $\Sigma$. In this paper, we define spaces ${\rm Q}^{D,\Sigma}_n(\Bbb
F)$ ($\Bbb F=\Bbb R$ or $\Bbb C$) which are real analogues of ${\rm
Poly}^{D,\Sigma}_n(\Bbb F)$ and which can be viewed as a generalizations of
spaces considered by Arnold, Vassiliev and others in the context of real
singularity theory. We prove that homotopy stability holds for these spaces and
compute the stability dimensions explicitly.
