The electrostatic probe technique has been used extensively in experimental investigations of plasma properties. There exists a well developed theory of stationary systems but little work seems to have been done on the cases where time dependence is not negligible. In the present paper, a technique is described which is suitable for situations in which timevariation is significant. A time-dependent probe theory is set up, so that measurements made using the method can be related to the internal properties of the plasma. The particular problem considered is that of a flame front traversing a narrow passage. Two cases are considered: (i) the passage is of rectangular cross-section, with pairs of electrostatic probes set in opposite walls; (ii) the passage is of annular cross-section, with sections of the inner and outer walls being used as probes. As the flame front passes them, the probes, in both cases, collect from the ionized gas a current which varies in time. The flame gas is considered to be a three-component plasma, and a set of time-dependent partial differential equations governing the collection of charged particles is derived. These are linearized and then solved using the Laplace transformation method. This gives a solution of the problem in the form of a generalized Fourier series. Approximations are made to the series solution to permit the calculation of the free stream ion density from the electric charge collected by the probe as the flame front sweeps past it. The value found in this way compares favourably with empirical results.