  A $(k_1+k_2)$-bispindle is the union of $k_1$ $(x,y)$-dipaths and $k_2$
$(y,x)$-dipaths, all these dipaths being pairwise internally disjoint.
Recently, Cohen et al. showed that for every $(1,1)$- bispindle $B$, there
exists an integer $k$ such that every strongly connected digraph with chromatic
number greater than $k$ contains a subdivision of $B$. We investigate
generalisations of this result by first showing constructions of strongly
connected digraphs with large chromatic number without any $(3,0)$-bispindle or
$(2,2)$-bispindle. Then we show that strongly connected digraphs with large
chromatic number contains a $(2,1)$-bispindle, where at least one of the
$(x,y)$-dipaths and the $(y,x)$-dipath are long.
