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We continue our study of the topology of the spaces of $m$ tuples of realpolynomials with common degree $d$ and without common roots of multiplicity$n$, and in particular their stability properties with respect to $d$. In anearlier paper we have proved a homotopy stability result and determined thestable homotopy types of such spaces in the case $m n >=4$. In the case $m n=3$ we could only prove stability in homology. In this paper we prove thecorresponding homotopy result for the case $(m,n)=(3,1)$. in the appendix wealso deal with the case ${m,n)={1,2}$.

Homotopy stability of spaces of non-resultant systems of bounded multiplicity with real coefficients