Low-temperature plasmas are frequently not in thermodynamic equilibrium. External fields, the emission of radiation, gradients of various physical properties, and the finite rates of various processes can all prevent the attainment of equilibrium. In nonequilibrium conditions the ionization state, the distribution of atomic excited states, and the electron energy distribution all become complicated functions of the factors responsible for the deviation from equilibrium. Since the components of the plasma--the electrons, atoms, and ions--are strongly coupled, a departure from equilibrium in one component causes departure in the others. The criteria for a deviation from local thermodyamic equilibrium are given. A study is made of plasmas far from equilibrium, in which the electron density is not described by the Saha equation, the atoms do not have a Boltzmann energy-level distribution, and the electrons do not have a Maxwellian energy distribution. A steady-state nonequilibrium plasma and time-dependent relaxation phenomena are studied. The theory is compared with the extensive experimental data available.