The plasma line overshoot, which is observed at Arecibo during ionospheric-modification experiments, can be explained by propagation of Langmuir waves (L waves) trapped in magnetic field-aligned ducts. The miniovershoot, i.e., the early phase of the overshoot, results from the growth of L waves to saturation within a few milliseconds of transmitter turn-on ducts developed during previous transmitter-on cycles. The ponderomotive force of these trapped L waves causes the electron density in the duct to decrease rapidly from about 30 to 200 ms after transmitter turn-on. An increase in plasma line (PL) intensity is assumed to result from this density decrease and this corresponds to the start of the main overshoot. After a few hundred milliseconds heating of the electrons begins to cause a further slow decrease in density. The heating is due to collisional and collisionless damping of the L waves. After a few seconds the duct density becomes sufficiently low that collisionless damping of the L waves responsible for the PL becomes severe and the PL intensity decreases. The ponderomotive forces is maintained by other trapped L waves. Once the transmitter has been turned off the duct at first decays rapidly due to the removal of the ponderomotive force and then more slowly (10 to tens of seconds) due to both parallel and inward radial (i.e., perpendicular to the magnetic field) diffusion of plasma. The duct model can explain nearly all the observed characteristics of the PL observed at Arecibo; other theories and models cannot. ¿ American Geophysical Union 1988