Pulsation period of Cepheids should change as stars evolve through the instability strip. Rates of these changes found by other authors based on the decades-long O −C diagrams show rather good agreement with theoretical predictions. We have checked the variability on the scale of a few years on the data recently published by the Optical Gravitational Lensing Experiment (OGLE) for the Large Magellanic Cloud Cepheids and found period changes for 18% of fundamental mode and 41% of first overtone pulsators. It suggest the overtone pulsations are less stable than the fundamental ones. For stars which had the cross-references in the MACHO catalog we have checked if the period change rates derived from the OGLE and the MACHO data are consistent. It was found that there is no correlation and opposite signs of changes in both data sets are more common than the same ones. Many O−C diagrams show nonlinear period changes similarly as for some stars the diagrams derived from the OGLE data only (spanning up to 4100 days) show random fluctuations. These fluctuations are common on the long-term O−C diagrams and we conclude they dominate the diagrams for the timescales of a few thousand of days. The distributions of periods and colors for all Cepheids and for those with statistically significant period changes are the same. Times of maximum light obtained using the MACHO and the OGLE data as well as the examples of O−C diagrams are presented.