  We give an upper bound for the rank $r$ of homogeneous (even) Clifford
structures on compact manifolds of non-vanishing Euler characteristic. More
precisely, we show that if $r=2^a\cdot b$ with $b$ odd, then $r\le 9$ for
$a=0$, $r\le 10$ for $a=1$, $r\le 12$ for $a=2$ and $r\le 16$ for $a\ge 3$.
Moreover, we describe the four limiting cases and show that there is exactly
one solution in each case.
