1. The resistance of Klebsiella pneumoniae to amikacin and gentamicin was studied by a mathematical model to predict the rate of sensitivity decrease. The results accurately matched experimental data, showing that the model is a reliable predicting tool. 2. The observations were carried out over six years and included 2677 cultures that were positive for K. pneumoniae. At the beginning of the observation period, 85.7% of the cultures were sensitive to amikacin and 40.8% were sensitive to gentamicin. Sensitivity to amikacin showed a surprisingly rapid decrease; at the end of the experimental period, amikacin and gentamicin sensitivities were 33.3% and 27.8%, respectively. 3. We conclude that patterns of resistance of other bacteria could be investigated using this method.