  Let $V(n,k,s)$ be the set of $k$-subsets $S$ of $[n]$ such that for all
$i,j\in S$, we have $|i-j|\geq s$ We define almost $s$-stable Kneser hypergraph
$KG^r{{[n]}\choose k}_{s{\tiny{\textup{-stab}}}}^{\displaystyle\sim}$ to be the
$r$-uniform hypergraph whose vertex set is $V(n,k,s)$ and whose edges are the
$r$-uples of disjoint elements of $V(n,k,s)$.
  With the help of a $Z_p$-Tucker lemma, we prove that, for $p$ prime and for
any $n\geq kp$, the chromatic number of almost 2-stable Kneser hypergraphs
$KG^p {{[n]}\choose k}_{2{\tiny{\textup{-stab}}}}^{\displaystyle\sim}$ is equal
to the chromatic number of the usual Kneser hypergraphs $KG^p{{[n]}\choose k}$,
namely that it is equal to $\lceil\frac{n-(k-1)p}{p-1}\rceil.$
  Defining $\mu(r)$ to be the number of prime divisors of $r$, counted with
multiplicities, this result implies that the chromatic number of almost
$2^{\mu(r)}$-stable Kneser hypergraphs $KG^r{{[n]}\choose
k}_{2^{\mu(r)}{\tiny{\textup{-stab}}}}^{\displaystyle\sim}$ is equal to the
chromatic number of the usual Kneser hypergraphs $KG^r{{[n]}\choose k}$ for any
$n\geq kr$, namely that it is equal to $\lceil\frac{n-(k-1)r}{r-1}\rceil.$
