  In the framework of type II seesaw mechanism we discuss the number of sterile
right-handed Majorana neutrinos being the warm dark matter (WDM). When the type
II seesaw mass term $M_\nu ^{II}$ is far less than the type I seesaw mass term
$M_\nu ^{I}$, only one of three sterile neutrinos may be the WDM particle. On
the contrary, the WDM particles may contain all sterile neutrinos. If $M_\nu
^{II} \sim M_\nu ^{I}$, the allowed number is not more than $N - 1$ for $N$
sterile neutrinos. It is worthwhile to stress that three different types of
neutrino mass spectrum are permitted when $M_\nu ^{II} \gg M_\nu ^{I}$ and
$M_\nu ^{II} \sim M_\nu ^{I}$.
