  Ferromagnetism with high Curie temperature $T_c$, well above room
temperature, and very small saturation moment has been reported in various
carbon and boron systems. It is argued that the magnetization must be very
inhomogeneous with only a small fraction of the sample ferromagnetically
ordered. It is shown that a possible source of high $T_c$ within the
ferromagnetic regions is itinerant electrons occupying a narrow impurity band.
Correlation effects do not reduce the effective interaction which enters the
Stoner criterion in the same way as in a bulk band. It is also shown how, in
the impurity band case, spin wave excitations may not be effective in lowering
$T_c$ below its value given by Stoner theory. These ideas are applied to
CaB$_6$ and a thorough review of the experimental situation in this material is
given. It is suggested that the intrinsic magnetism of the B$_2$ and O$_2$
dimers might be exploited in suitable structures containing these elements.
