  Let $M$ be a closed K-contact $(2n+1)$-manifold equipped with a quasi-regular
K-contact structure. Rukimbira proved that the Reeb vector field $\xi$ of this
structure has at least $n+1$ closed characteristics. We note that $\xi$ has at
least $2n+1$ closed characteristics provided that the space of leaves of the
foliation determined by $\xi$ is symplectically aspherical.
