Abstract The proliferation rate of various cell types in vitro, including hepatoma Fao cells, displays aperiodic oscillations. The frequency of these oscillations is about one every 3–5 weeks, and there are variations in cell functions and polarity. Topological analysis has showed that these oscillations in growth rate are determined, and presumably chaotic. One characteristic of complex chaotic systems is that their dynamics can be persistently modified by a small external perturbation. We show that treatment with a single small dose of the anticancer drug methotrexate causes long-term stable alteration of the oscillatory dynamics of Fao cell proliferation. The oscillations of growth rate are shifted, and their mean level decreased according to a fractal pattern.