Using the concept of an anisotropic plasma as a working hypothesis, a stress tensor has been constructed that is determined by five independent coefficients. As an application the general expression for the dispersion relation is derived. Under certain limiting conditions it was found that the plasma mode &ohgr;2&egr;=(4&pgr;&eegr;&egr;e2)/m&egr;decays exponentially because of thec33coefficient, with a decay time &tgr;33=2&rgr;0/c33k2.