Measurements were made of the "head inhibition" and the "head inhibition gradient" in Hydra. Following decapitation, the head inhibition decays with a half-time of 2-3 hr. The slope of the inhibition gradient increases about twofold when the temperature is raised from 20 to 24 degrees C; the increase (at the higher temperature) occurs with a half-time of about 1.2 hr. These results are consistent with the idea that the head inhibition and the head inhibition gradient are due to a diffusing substance, made in the head and broken down in the body of Hydra, with a half-life of about 2 hr at 20 degrees C and about 1 hr at 24 degrees C. Calculations suggest a diffusion constant of 1-3 X 10(-6) cm2/sec and a gradient range (ratio of maximum to minimum concentration) of about 2. During head regeneration, the head inhibition returns much more slowly than one would expect if its production were switched on at the time of "head determination." The slow return of the inhibition can be explained if one assumes that determination is due to the "activation" of a few cells, while the restoration of inhibition depends on the lateral expansion of the activated region. This behavior is observed in a "proportion-regulating" diffusion-reaction model proposed by Gierer and Meinhardt, 1972, Kybernetik 12, 30-39. Transplants to beheaded animals demonstrate a substantial inhibition gradient even at 6 hr after decapitation, a time at which most of the inhibitor from the original head should have decayed and no substantial amount of inhibitor is expected from the regenerated head. Experiments in which parts of a hydra's body are removed suggest that this inhibition gradient is due to the production of some inhibitor in the body, with larger amounts produced in apical portions.