Within the framework of the continuum elastic theory of biaxial nemati
c liquid crystals, we have addressed ourselves to the structure, stabi
lity and energetics of some singular and non-singular topological defe
cts, and certain director configurations. We find that certain nonsing
ular hybrid disclinations could be energetically favourable relative t
o certain half-strength disclinations. The interaction between singula
r hybrids depends strongly on the biaxial elastic anisotropy. We sugge
st possible defect structures that can exist in spherical droplets of
biaxial nematics. Further we find structural instabilities, in confine
d geometries, arising due to the inherent biaxiality of the system.