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Disturbance of the Maxwellian plasma may occur in the vicinity of a spacecraft due to photoemission, interactions between the spacecraft and thermospheric gases, or electron emissions from other devices on the spacecraft. Significant non-maxwellian plasma distributions may also occur in nature as a mixture of ionospheric and magnetospheric plasmas or secondaries produced by photoionization in the thermosphere or auroral precipitation. The general formulas for current collection (volt-ampere curves) by planar, cylindrical, and spherical Langmuir probes in isotropic and anisotropic non-maxwellian plasmas are examined. Examples are given of how one may identify and remove the non-maxwellian components in the Langmuir probe current to permit the ionospheric parameters to be determined. Theoretical volt-ampere curves presented for typical examples of non-maxwellian distributions include: two-temperature plasmas and a thermal plasma with an energetic electron beam. If the non-ionospheric electrons are Maxwellian at a temperature distinct from that of the ionosphere electrons, the volt-ampere curves can be fitted directly to obtain the temperatures and densities of both electron components without resorting to differenting the current. For an arbitrary isotropic distribution, the current for retarded particles is shown to be identical for the three geometries. For anisotropic distributions, the three probe geometries are not equally suited for measuring the ionospheric electron temperature and density or for determining the distribution function in the presence of non-maxwellian back-round electrons.