The mathematical problem of transient currents that are produced by space‐charge swarms after they are injected into liquids or gases is solved using a field‐independent mobility model for the charge carriers. Only one species of charge carrier is assumed to be present in the fluid‐containing drift space defined by parallel‐plane constant potential electrodes. An integral‐differential equation is derived for arbitrary initial charge distributions in the drift space. From its solution, the transient current waveform can be determined. When the initial current is in a steady state, the integral‐differential equation reduces to a nonlinear ordinary differential equation which is valid for initial currents that may or may not be space‐charge limited. This final equation is solved for the special case of small space‐charge fields. The analysis is also expected to apply to conduction in solids in some cases.