Anisotropic systems of quarks and gluons, which at least for sufficiently s
hort space-time intervals can be treated as homogeneous and static, an cons
idered. The gluon polarization tensor of such a system is explicitly comput
ed within the semiclassical kinetic and hard loop diagrammatic theories. Th
e equivalence of the two approaches is demonstrated. The quark self-energy
is computed as well, and finally, the dispersion relations of quarks and gl
uons in the anisotropic medium are discussed.