Linearized equations are derived for disturbances in an infinite plasma without an imposed magnetic field. It is shown that besides the electrostatic, or longitudinal, waves which are usually considered, there can also exist electromagnetic, or transverse, waves. The two sets of waves are generally coupled, but one can nevertheless classify the waves as either mainly longitudinal or mainly transverse. It turns out that a plasma which is stable to longitudinal waves will be unstable to transverse waves unless the velocity distribution of its particles satisfies some rather stringent conditions. In a practical case these conditions would require the distribution to be isotropic.